# Heavy vs. light flowers # Callin Switzer # 12 October 2016 # update 8 Dec 2017 # # Compares the bees' frequency when they are buzzing on # heavy (metal added) vs. light flowers # Note: all pores were glued shut
#install packages
ipak <- function(pkg){
new.pkg <- pkg[!(pkg %in% installed.packages()[, "Package"])]
if(length(new.pkg)) install.packages(new.pkg, dependencies = TRUE)
sapply(pkg, require, character.only = TRUE)
}
packages <- c("ggplot2", "reshape2", 'lme4', 'sjPlot', "multcomp", "plyr", "effects", "gamm4", "viridis",
"cowplot")
ipak(packages)## Loading required package: ggplot2## Loading required package: reshape2## Loading required package: lme4## Loading required package: Matrix## Loading required package: sjPlot## Warning in checkMatrixPackageVersion(): Package version inconsistency detected.
## TMB was built with Matrix version 1.2.10
## Current Matrix version is 1.2.11
## Please re-install 'TMB' from source or restore original 'Matrix' package## #refugeeswelcome## Loading required package: multcomp## Loading required package: mvtnorm## Loading required package: survival## Loading required package: TH.data## Loading required package: MASS##
## Attaching package: 'TH.data'## The following object is masked from 'package:MASS':
##
## geyser## Loading required package: plyr## Loading required package: effects## Loading required package: carData## lattice theme set by effectsTheme()
## See ?effectsTheme for details.## Loading required package: gamm4## Loading required package: mgcv## Loading required package: nlme##
## Attaching package: 'nlme'## The following object is masked from 'package:lme4':
##
## lmList## This is mgcv 1.8-20. For overview type 'help("mgcv-package")'.## This is gamm4 0.2-5## Loading required package: viridis## Loading required package: viridisLite## Loading required package: cowplot##
## Attaching package: 'cowplot'## The following object is masked from 'package:sjPlot':
##
## plot_grid## The following object is masked from 'package:ggplot2':
##
## ggsave## ggplot2 reshape2 lme4 sjPlot multcomp plyr effects gamm4
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## viridis cowplot
## TRUE TRUE# set ggplot theme
theme_set(theme_classic() + theme(axis.text=element_text(colour="black")))
# define data and figure directories
dataDir <- "/Users/cswitzer/Dropbox/SonicationBehavior/SonBehData"
figDir <- "/Users/cswitzer/Dropbox/SonicationBehavior/SonBehFigs"
# print system info
print(paste("last run ", Sys.time()))## Warning in as.POSIXlt.POSIXct(x, tz): unknown timezone 'zone/tz/2018c.1.0/
## zoneinfo/America/Los_Angeles'## [1] "last run 2018-02-14 22:13:14"print(R.version)## _
## platform x86_64-apple-darwin15.6.0
## arch x86_64
## os darwin15.6.0
## system x86_64, darwin15.6.0
## status
## major 3
## minor 4.2
## year 2017
## month 09
## day 28
## svn rev 73368
## language R
## version.string R version 3.4.2 (2017-09-28)
## nickname Short SummerRead in data and do some visualizations
new_df = read.csv(file.path(dataDir, "02_HeavyLight_cleaned.csv"))
# divide amplitude by two
new_df$amp = new_df$amp / 2
new_df$amp_acc = new_df$amp_acc / 2
new_df$hive = as.factor(new_df$hive)
new_df$treatment <- mapvalues(new_df$treatment, from = c("sham", "weighted"), to = c("Sham", "Weighted"))
head(new_df)## freq amp datetime rewNum
## 1 250 0.089725 2016_09_28__09_59_13_112 1
## 2 300 0.283285 2016_09_28__09_59_14_520 2
## 3 400 0.341855 2016_09_28__09_59_15_030 3
## 4 410 0.400590 2016_09_28__09_59_15_707 4
## 5 370 0.263330 2016_09_28__09_59_16_277 5
## 6 360 0.157705 2016_09_28__09_59_17_096 6
## accFile beeID hive IT
## 1 2016_09_28__09_59_13_112_220_450_test.txt 7 3 3.98
## 2 2016_09_28__09_59_14_520_220_450_test.txt 7 3 3.98
## 3 2016_09_28__09_59_15_030_220_450_test.txt 7 3 3.98
## 4 2016_09_28__09_59_15_707_220_450_test.txt 7 3 3.98
## 5 2016_09_28__09_59_16_277_220_450_test.txt 7 3 3.98
## 6 2016_09_28__09_59_17_096_220_450_test.txt 7 3 3.98
## accFileAndFolder
## 1 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## 2 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## 3 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## 4 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## 5 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## 6 Bee7_28Sept2016_Hive3_S_W/2016_09_28__09_58_58_ampFreq.txt
## dateFrozenOrMarked treatment amp_acc
## 1 28-Sep-16 Sham 8.822517
## 2 28-Sep-16 Sham 27.854966
## 3 28-Sep-16 Sham 33.614061
## 4 28-Sep-16 Sham 39.389381
## 5 28-Sep-16 Sham 25.892822
## 6 28-Sep-16 Sham 15.506883# calculate average number of each treatment
ll = list(tapply(new_df$treatment, new_df$beeID, table))
dd = data.frame(unlist(ll))
dd$beeTrt = row.names(dd)
dd$beeID = sapply(dd$beeTrt, FUN = function(x) strsplit(x, "\\.")[[1]][1])
dd$trt = sapply(dd$beeTrt, FUN = function(x) strsplit(x, "\\.")[[1]][2])
# shows average number of buzzes per treatment
tapply(dd$unlist.ll., INDEX = dd$trt, mean)## Sham Weighted
## 29.69444 35.86111tapply(dd$unlist.ll., INDEX = dd$trt, sd) # sd for number of buzzes## Sham Weighted
## 9.603034 15.224328# show histograms of frequencies
hist(new_df$freq, breaks = seq(215, 455, by = 10))
# Calculate average for each bee and for each treatment
frqMeans <- as.data.frame(tapply(X = new_df$freq, INDEX = list(new_df$beeID, new_df$treatment), mean))
frqMeans$beeID <- row.names(frqMeans)
frqMeans## Sham Weighted beeID
## 1 344.3333 347.0833 1
## 10 331.2000 382.5000 10
## 11 411.7391 387.6923 11
## 12 344.8276 339.2500 12
## 14 324.0625 281.6000 14
## 15 367.5000 376.3158 15
## 16 357.0588 386.0606 16
## 17 314.0741 341.6000 17
## 18 366.4706 345.0000 18
## 19 375.0000 379.2308 19
## 2 298.5294 322.9167 2
## 20 359.8148 313.3333 20
## 21 331.3158 310.7143 21
## 22 399.4286 388.2857 22
## 23 348.2759 351.2821 23
## 24 287.7778 273.3333 24
## 25 345.0000 352.3684 25
## 26 369.6000 392.7273 26
## 27 366.6667 350.0000 27
## 28 364.4444 374.1935 28
## 29 291.2500 319.3333 29
## 3 399.0323 388.9655 3
## 30 368.0769 369.0323 30
## 31 273.5294 320.4167 31
## 32 325.6000 246.1538 32
## 4 356.6667 371.3636 4
## 5 370.7692 353.7143 5
## 6 284.2857 326.5714 6
## 7 366.9697 396.3415 7
## 8 333.8462 342.0833 8
## 9 344.4000 384.4444 9
## blue 319.1429 333.8462 blue
## gold 374.5098 365.2174 gold
## orange 309.6875 319.1000 orange
## pink 385.3333 367.5000 pink
## white 319.7674 326.9444 white# convert to long format for ggplot-ing
frqLong <- melt(frqMeans, id.vars = "beeID", measure.vars = c("Sham", "Weighted"),
variable.name = "trt", value.name = "frq")
nrow(frqLong)## [1] 72ggplot(frqLong, aes(x = trt, y = frq)) +
geom_boxplot() +
geom_line(aes(group = beeID))+
geom_point()
ggplot(frqLong, aes(x = trt, y = frq)) +
geom_boxplot() +
labs(y = "Buzz Frequency (Hz)", x = "Flower treatment")
#ggsave(file.path(figDir, "heavyLight_frq.pdf"), width = 5, height = 4)
# print some descriptive statistics
nrow(new_df)## [1] 2360unique(new_df$hive)## [1] 3 4
## Levels: 3 4# Calculate average amplitude for each bee and for each treatment
ampMeans <- as.data.frame(tapply(X = new_df$amp_acc, INDEX = list(new_df$beeID, new_df$treatment), mean))
ampMeans$beeID <- row.names(ampMeans)
ampMeans## Sham Weighted beeID
## 1 39.70744 24.541216 1
## 10 24.22769 15.418649 10
## 11 17.28190 11.444180 11
## 12 19.84847 18.109710 12
## 14 14.03120 11.075556 14
## 15 21.92283 19.648515 15
## 16 25.04022 18.327225 16
## 17 19.29140 17.107994 17
## 18 15.78372 11.735532 18
## 19 21.83492 12.326778 19
## 2 17.55835 17.037781 2
## 20 23.69995 17.697342 20
## 21 22.35682 17.249210 21
## 22 16.18466 12.351271 22
## 23 31.71900 23.023864 23
## 24 20.68468 11.487934 24
## 25 18.39199 10.026018 25
## 26 14.04610 11.081419 26
## 27 19.83488 15.451298 27
## 28 22.37161 19.972849 28
## 29 21.66900 11.190888 29
## 3 24.51342 28.123419 3
## 30 27.23703 14.518762 30
## 31 28.58787 15.258931 31
## 32 17.51064 2.504690 32
## 4 17.42392 18.981094 4
## 5 25.68650 16.483677 5
## 6 12.53034 18.368043 6
## 7 21.15394 23.764216 7
## 8 35.76728 14.135488 8
## 9 19.39762 14.562639 9
## blue 15.91575 9.797935 blue
## gold 17.36498 10.433586 gold
## orange 26.41613 23.003918 orange
## pink 15.31175 19.774079 pink
## white 11.27583 7.690511 whiteampLong <- melt(ampMeans, id.vars = "beeID", measure.vars = c("Sham", "Weighted"),
variable.name = "trt", value.name = "amp")
ggplot(ampLong, aes(x = trt, y = amp)) +
geom_boxplot() +
geom_point() +
labs(y = expression ("Sonication acceleration "(m~s^{-2})), x = "Flower treatment")
ggplot(ampLong, aes(x = trt, y = amp)) +
geom_boxplot() +
geom_point() +
geom_line(aes(group = beeID))
ggplot(ampLong, aes(x = trt, y = amp)) +
geom_boxplot() +
labs(y = expression ("Sonication acceleration "(m~s^{-2})), x = "Flower treatment")
#ggsave(file.path(figDir, 'heavyLightAmp.pdf'), width = 5, heigh = 4)
nrow(ampLong)## [1] 72Modeling frequency with GAMM
Use BIC to select model (decide what interactions and covariates to use)
Make sure that REML = FALSE when comparing BIC values
Start with the biggest model of interest, and then see what predictors can be removed
rr = new_df$treatment[1]
df1 = new_df[1, ]
for(ii in 1:(nrow(new_df) -1)){
if(rr == new_df$treatment[ii + 1]) next
else{
df1 = rbind(df1, new_df[ii+1, ])
rr = new_df$treatment[ii + 1]
}
}
df1 <- df1[df1$rewNum != 1, ]
df1$trtSwitch = df1$rewNum
colnames(df1)## [1] "freq" "amp" "datetime"
## [4] "rewNum" "accFile" "beeID"
## [7] "hive" "IT" "accFileAndFolder"
## [10] "dateFrozenOrMarked" "treatment" "amp_acc"
## [13] "trtSwitch"df2 <- df1[, c("beeID", "hive", "trtSwitch", "IT")]
df2## beeID hive trtSwitch IT
## 34 7 3 34 3.98
## 111 white 3 37 3.70
## 178 1 4 25 4.07
## 232 8 4 25 3.84
## 284 19 3 27 4.01
## 353 29 3 31 3.78
## 402 16 3 34 4.11
## 478 26 3 26 3.72
## 536 32 3 26 3.72
## 573 15 4 25 3.61
## 635 24 4 25 3.55
## 687 10 3 26 4.09
## 745 30 4 27 4.19
## 814 21 3 39 3.52
## 897 28 4 28 3.57
## 963 6 3 36 4.55
## 1002 orange 3 33 4.81
## 1129 17 4 28 4.25
## 1205 25 3 27 3.73
## 1267 31 3 25 3.76
## 1336 blue 3 36 3.91
## 1391 23 3 30 4.18
## 1459 12 3 30 4.10
## 1530 3 3 32 4.27
## 1594 22 4 36 3.65
## 1673 4 3 45 4.27
## 1710 9 3 26 4.17
## 1763 5 3 27 3.76
## 1832 2 4 35 4.42
## 1930 11 3 27 3.92
## 1986 20 3 34 4.28
## 2065 14 4 26 4.23
## 2127 pink 4 31 4.29
## 2204 27 3 34 3.51
## 2253 18 3 29 3.12
## 2310 gold 3 24 4.13sum(duplicated(df2$beeID))## [1] 0newdf2 <- merge(new_df, df2)
head(newdf2)## beeID hive IT freq amp datetime rewNum
## 1 1 4 4.07 310 0.326120 2016_09_27__10_52_32_696 1
## 2 1 4 4.07 330 0.238665 2016_09_27__10_52_41_293 2
## 3 1 4 4.07 240 0.275335 2016_09_27__10_52_42_247 3
## 4 1 4 4.07 290 0.144885 2016_09_27__10_52_42_974 4
## 5 1 4 4.07 360 0.236555 2016_09_27__10_52_51_809 5
## 6 1 4 4.07 360 0.226820 2016_09_27__10_53_00_124 6
## accFile
## 1 2016_09_27__10_52_32_696_220_450_test.txt
## 2 2016_09_27__10_52_41_293_220_450_test.txt
## 3 2016_09_27__10_52_42_247_220_450_test.txt
## 4 2016_09_27__10_52_42_974_220_450_test.txt
## 5 2016_09_27__10_52_51_809_220_450_test.txt
## 6 2016_09_27__10_53_00_124_220_450_test.txt
## accFileAndFolder
## 1 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 2 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 3 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 4 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 5 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 6 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## dateFrozenOrMarked treatment amp_acc trtSwitch
## 1 27-Sep-16 Weighted 32.06686 25
## 2 27-Sep-16 Weighted 23.46755 25
## 3 27-Sep-16 Weighted 27.07325 25
## 4 27-Sep-16 Weighted 14.24631 25
## 5 27-Sep-16 Weighted 23.26008 25
## 6 27-Sep-16 Weighted 22.30285 25newdf2$visitNum_centered <- newdf2$rewNum - newdf2$trtSwitch
# get treatment
trts <- (sapply(unique(newdf2$beeID), FUN = function(x){
startt = newdf2[newdf2$beeID == x & newdf2$rewNum == 1, "treatment" ]
return(as.character(startt))
}))
df4 <- data.frame(beeID = unique(newdf2$beeID), trts = trts)
newdf3 <- merge(newdf2, df4)
newdf3$trt2 <- as.factor(paste(newdf3$trts, "first"))
head(newdf3)## beeID hive IT freq amp datetime rewNum
## 1 1 4 4.07 310 0.326120 2016_09_27__10_52_32_696 1
## 2 1 4 4.07 330 0.238665 2016_09_27__10_52_41_293 2
## 3 1 4 4.07 240 0.275335 2016_09_27__10_52_42_247 3
## 4 1 4 4.07 290 0.144885 2016_09_27__10_52_42_974 4
## 5 1 4 4.07 360 0.236555 2016_09_27__10_52_51_809 5
## 6 1 4 4.07 360 0.226820 2016_09_27__10_53_00_124 6
## accFile
## 1 2016_09_27__10_52_32_696_220_450_test.txt
## 2 2016_09_27__10_52_41_293_220_450_test.txt
## 3 2016_09_27__10_52_42_247_220_450_test.txt
## 4 2016_09_27__10_52_42_974_220_450_test.txt
## 5 2016_09_27__10_52_51_809_220_450_test.txt
## 6 2016_09_27__10_53_00_124_220_450_test.txt
## accFileAndFolder
## 1 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 2 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 3 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 4 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 5 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## 6 Bee1_27Sept_Hive4_W_S/2016_09_27__10_52_05_ampFreq.txt
## dateFrozenOrMarked treatment amp_acc trtSwitch visitNum_centered
## 1 27-Sep-16 Weighted 32.06686 25 -24
## 2 27-Sep-16 Weighted 23.46755 25 -23
## 3 27-Sep-16 Weighted 27.07325 25 -22
## 4 27-Sep-16 Weighted 14.24631 25 -21
## 5 27-Sep-16 Weighted 23.26008 25 -20
## 6 27-Sep-16 Weighted 22.30285 25 -19
## trts trt2
## 1 Weighted Weighted first
## 2 Weighted Weighted first
## 3 Weighted Weighted first
## 4 Weighted Weighted first
## 5 Weighted Weighted first
## 6 Weighted Weighted first# GAMM
# start with gamm so I can show change by visit number
g01 = gamm4(freq ~ s(visitNum_centered, by = trt2) + IT + hive + treatment + trt2, random = ~(1|beeID), data = newdf3)
par(mfrow = c(2,3))
aab <- plot(g01$gam, all.terms = TRUE, rug = FALSE, shade = TRUE)
summary(g01$gam) # Summary for paper ##
## Family: gaussian
## Link function: identity
##
## Formula:
## freq ~ s(visitNum_centered, by = trt2) + IT + hive + treatment +
## trt2
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 373.350 64.000 5.834 6.17e-09 ***
## IT -5.075 15.811 -0.321 0.748
## hive4 -4.208 11.433 -0.368 0.713
## treatmentWeighted 1.919 3.431 0.559 0.576
## trt2Weighted first -10.607 10.771 -0.985 0.325
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered):trt2Sham first 1 1 1.470 0.225
## s(visitNum_centered):trt2Weighted first 1 1 1.015 0.314
##
## R-sq.(adj) = -0.000401
## lmer.REML = 25097 Scale est. = 2354.9 n = 2360summary(g01$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 25096.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3193 -0.4698 0.1892 0.6934 2.3814
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 9.602e+02 3.099e+01
## Xr.0 s(visitNum_centered):trt2Weighted first 0.000e+00 0.000e+00
## Xr s(visitNum_centered):trt2Sham first 3.028e-11 5.503e-06
## Residual 2.355e+03 4.853e+01
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 373.350 64.000 5.834
## XIT -5.075 15.811 -0.321
## Xhive4 -4.208 11.433 -0.368
## XtreatmentWeighted 1.919 3.431 0.559
## Xtrt2Weighted first -10.607 10.771 -0.985
## Xs(visitNum_centered):trt2Sham firstFx1 2.285 1.885 1.212
## Xs(visitNum_centered):trt2Weighted firstFx1 2.569 2.550 1.007
##
## Correlation of Fixed Effects:
## X(Int) XIT Xhive4 XtrtmW Xtr2Wf X(N_):2Sf
## XIT -0.992
## Xhive4 -0.043 -0.011
## XtrtmntWght -0.041 0.011 0.003
## Xtrt2Wghtdf -0.237 0.165 -0.014 0.051
## X(N_):2SfF1 0.049 -0.028 -0.008 -0.707 -0.038
## X(N_):2WfF1 -0.032 0.012 -0.002 0.658 0.063 -0.466dev.off()## null device
## 1g02 = gamm4(freq ~ s(visitNum_centered, by = trt2) + hive + treatment + trt2, random = ~(1|beeID), data = newdf3)
anova(g01$mer, g02$mer) #g02 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g02$mer: NULL
## g01$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g02$mer 10 25152 25210 -12566 25132
## g01$mer 11 25154 25218 -12566 25132 0.1168 1 0.7325summary(g02$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 25104.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3173 -0.4693 0.1882 0.6954 2.3808
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 9.331e+02 3.055e+01
## Xr.0 s(visitNum_centered):trt2Weighted first 0.000e+00 0.000e+00
## Xr s(visitNum_centered):trt2Sham first 1.379e-10 1.174e-05
## Residual 2.355e+03 4.853e+01
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 352.967 7.981 44.23
## Xhive4 -4.248 11.276 -0.38
## XtreatmentWeighted 1.939 3.431 0.57
## Xtrt2Weighted first -10.030 10.478 -0.96
## Xs(visitNum_centered):trt2Sham firstFx1 2.262 1.884 1.20
## Xs(visitNum_centered):trt2Weighted firstFx1 2.583 2.550 1.01
##
## Correlation of Fixed Effects:
## X(Int) Xhive4 XtrtmW Xtr2Wf X(N_):2Sf
## Xhive4 -0.426
## XtrtmntWght -0.242 0.004
## Xtrt2Wghtdf -0.587 -0.012 0.051
## X(N_):2SfF1 0.171 -0.009 -0.707 -0.034
## X(N_):2WfF1 -0.158 -0.002 0.658 0.063 -0.466g03 = gamm4(freq ~ s(visitNum_centered, by = trt2) + hive + trt2, random = ~(1|beeID), data = newdf3)
anova(g02$mer, g03$mer) #g03 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g03$mer: NULL
## g02$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g03$mer 9 25151 25203 -12566 25133
## g02$mer 10 25152 25210 -12566 25132 0.328 1 0.5668summary(g03$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 25109
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3127 -0.4673 0.1923 0.6924 2.3917
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 935.9 30.59
## Xr.0 s(visitNum_centered):trt2Weighted first 0.0 0.00
## Xr s(visitNum_centered):trt2Sham first 0.0 0.00
## Residual 2354.1 48.52
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 354.059 7.754 45.66
## Xhive4 -4.271 11.292 -0.38
## Xtrt2Weighted first -10.330 10.479 -0.99
## Xs(visitNum_centered):trt2Sham firstFx1 3.015 1.332 2.26
## Xs(visitNum_centered):trt2Weighted firstFx1 1.635 1.919 0.85
##
## Correlation of Fixed Effects:
## X(Int) Xhive4 Xtr2Wf X(N_):2Sf
## Xhive4 -0.438
## Xtrt2Wghtdf -0.593 -0.012
## X(N_):2SfF1 0.000 -0.008 0.003
## X(N_):2WfF1 0.002 -0.005 0.039 0.000g04 = gamm4(freq ~ s(visitNum_centered, by = trt2) +trt2, random = ~(1|beeID), data = newdf3)
anova(g03$mer, g04$mer) # g04 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g04$mer: NULL
## g03$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g04$mer 8 25149 25195 -12566 25133
## g03$mer 9 25151 25203 -12566 25133 0.1558 1 0.693summary(g04$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 25115.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3139 -0.4690 0.1912 0.6937 2.3917
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 9.112e+02 3.019e+01
## Xr.0 s(visitNum_centered):trt2Weighted first 1.513e-09 3.890e-05
## Xr s(visitNum_centered):trt2Sham first 3.322e-12 1.823e-06
## Residual 2.354e+03 4.852e+01
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 352.774 6.883 51.25
## Xtrt2Weighted first -10.376 10.345 -1.00
## Xs(visitNum_centered):trt2Sham firstFx1 3.008 1.332 2.26
## Xs(visitNum_centered):trt2Weighted firstFx1 1.631 1.919 0.85
##
## Correlation of Fixed Effects:
## X(Int) Xtr2Wf X(N_):2Sf
## Xtrt2Wghtdf -0.665
## X(N_):2SfF1 -0.004 0.003
## X(N_):2WfF1 0.000 0.039 0.000g05 = gamm4(freq ~ s(visitNum_centered) +trt2, random = ~(1|beeID), data = newdf3)
anova(g04$mer, g05$mer) # g05 slightly better (according to BIC)## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g05$mer: NULL
## g04$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g05$mer 6 25145 25180 -12567 25133
## g04$mer 8 25149 25195 -12566 25133 0.3437 2 0.8421summary(g05$gam)##
## Family: gaussian
## Link function: identity
##
## Formula:
## freq ~ s(visitNum_centered) + trt2
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 352.783 6.875 51.312 <2e-16 ***
## trt2Weighted first -10.188 10.329 -0.986 0.324
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered) 1 1 5.478 0.0193 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = -0.00388
## lmer.REML = 25120 Scale est. = 2353.5 n = 2360g06 = gamm4(freq ~ s(visitNum_centered), random = ~(1|beeID), data = newdf3)
anova(g05$mer, g06$mer) # g05 slightly better (according to BIC)## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g06$mer: NULL
## g05$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g06$mer 5 25144 25173 -12567 25134
## g05$mer 6 25145 25180 -12567 25133 1.0153 1 0.3136summary(g06$mer) # g06 Better## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 25127.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3036 -0.4740 0.1917 0.6901 2.3998
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 9.078e+02 3.013e+01
## Xr s(visitNum_centered) 9.414e-11 9.703e-06
## Residual 2.354e+03 4.851e+01
## Number of obs: 2360, groups: beeID, 36; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 348.268 5.127 67.93
## Xs(visitNum_centered)Fx1 2.587 1.093 2.37
##
## Correlation of Fixed Effects:
## X(Int)
## Xs(vstN_)F1 0.018g07 = gamm4(freq ~ 1, random = ~(1|beeID), data = newdf3)
anova(g06$mer, g07$mer) # g07 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g07$mer: NULL
## g06$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g07$mer 3 25146 25163 -12570 25140
## g06$mer 5 25144 25173 -12567 25134 5.584 2 0.0613 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# looks like GAMM is not necessary -- no predictors significantly affect frequencyModeling frequency with lmer
Do a similar thing to GAMM above (but make it more interpretable)
# fit lmer that is similar to gamm above
# interaction that may be important, based on domain knowledge
m0 = lmer(freq ~ I(scale(visitNum_centered)) * trt2 + I(scale(IT)) * treatment + hive + I(scale(visitNum_centered^2)) + I(scale(IT)^2) + (1|beeID), data = newdf3, REML = FALSE)
summary(m0)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) * trt2 + I(scale(IT)) * treatment +
## hive + I(scale(visitNum_centered^2)) + I(scale(IT)^2) + (1 |
## beeID)
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25151.7 25220.8 -12563.8 25127.7 2348
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2909 -0.4690 0.2002 0.6886 2.3918
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 812.4 28.50
## Residual 2348.7 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 356.7188 8.2319 43.33
## I(scale(visitNum_centered)) 1.3722 2.4815 0.55
## trt2Weighted first -9.6850 9.9725 -0.97
## I(scale(IT)) -4.9677 5.4807 -0.91
## treatmentWeighted 2.9453 3.7036 0.80
## hive4 -4.9106 10.5727 -0.46
## I(scale(visitNum_centered^2)) 0.1972 1.5799 0.12
## I(scale(IT)^2) -5.2727 3.9217 -1.34
## I(scale(visitNum_centered)):trt2Weighted first 1.1188 4.2882 0.26
## I(scale(IT)):treatmentWeighted 3.8345 2.2161 1.73
##
## Correlation of Fixed Effects:
## (Intr) I((N_) trt2Wf I(s(IT)) trtmnW hive4 I((N_^ I((IT)^
## I(scl(vN_)) 0.192
## trt2Wghtdfr -0.504 -0.048
## I(scal(IT)) -0.062 0.040 0.150
## trtmntWghtd -0.257 -0.742 0.061 -0.034
## hive4 -0.411 -0.020 -0.017 -0.005 0.011
## I(sc(N_^2)) -0.071 -0.623 0.032 -0.036 0.350 0.016
## I(sc(IT)^2) -0.400 -0.009 -0.068 0.128 0.007 0.059 -0.036
## I((N_)):2Wf -0.214 -0.842 0.070 -0.015 0.821 0.013 0.448 0.018
## I(sc(IT)):W -0.034 -0.171 -0.001 -0.236 0.136 0.005 -0.026 -0.029
## I((N_f
## I(scl(vN_))
## trt2Wghtdfr
## I(scal(IT))
## trtmntWghtd
## hive4
## I(sc(N_^2))
## I(sc(IT)^2)
## I((N_)):2Wf
## I(sc(IT)):W 0.088# no interaction
m1 = update(m0, .~. - I(scale(visitNum_centered^2)))
BIC(m0, m1) # stay with m1 -- no interaction## df BIC
## m0 12 25220.85
## m1 11 25213.10anova(m0, m1) # agrees with BIC## Data: newdf3
## Models:
## m1: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m1: hive + I(scale(IT)^2) + (1 | beeID) + I(scale(visitNum_centered)):trt2 +
## m1: I(scale(IT)):treatment
## m0: freq ~ I(scale(visitNum_centered)) * trt2 + I(scale(IT)) * treatment +
## m0: hive + I(scale(visitNum_centered^2)) + I(scale(IT)^2) + (1 |
## m0: beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m1 11 25150 25213 -12564 25128
## m0 12 25152 25221 -12564 25128 0.0156 1 0.9007summary(m1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## hive + I(scale(IT)^2) + (1 | beeID) + I(scale(visitNum_centered)):trt2 +
## I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25149.7 25213.1 -12563.8 25127.7 2349
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2901 -0.4672 0.1999 0.6872 2.3924
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 812.2 28.50
## Residual 2348.7 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 356.792 8.210 43.46
## I(scale(visitNum_centered)) 1.565 1.940 0.81
## trt2Weighted first -9.725 9.966 -0.98
## I(scale(IT)) -4.943 5.477 -0.90
## treatmentWeighted 2.784 3.470 0.80
## hive4 -4.932 10.570 -0.47
## I(scale(IT)^2) -5.255 3.919 -1.34
## I(scale(visitNum_centered)):trt2Weighted first 0.879 3.833 0.23
## I(scale(IT)):treatmentWeighted 3.842 2.215 1.73
##
## Correlation of Fixed Effects:
## (Intr) I((N_) trt2Wf I(s(IT)) trtmnW hive4 I((IT)^ I((N_f
## I(scl(vN_)) 0.190
## trt2Wghtdfr -0.503 -0.036
## I(scal(IT)) -0.064 0.023 0.152
## trtmntWghtd -0.248 -0.716 0.053 -0.022
## hive4 -0.411 -0.013 -0.018 -0.005 0.006
## I(sc(IT)^2) -0.404 -0.040 -0.067 0.127 0.021 0.060
## I((N_)):2Wf -0.204 -0.805 0.062 0.001 0.793 0.006 0.038
## I(sc(IT)):W -0.036 -0.239 0.000 -0.237 0.155 0.005 -0.030 0.111m1.1 <- update(m1, .~. - I(scale(visitNum_centered)):trt2)
anova(m1.1, m1) # keep 1.1## Data: newdf3
## Models:
## m1.1: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m1.1: hive + I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## m1: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m1: hive + I(scale(IT)^2) + (1 | beeID) + I(scale(visitNum_centered)):trt2 +
## m1: I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m1.1 10 25148 25205 -12564 25128
## m1 11 25150 25213 -12564 25128 0.0526 1 0.8187summary(m1.1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## hive + I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25147.7 25205.4 -12563.9 25127.7 2350
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2923 -0.4665 0.2003 0.6857 2.3925
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 812.7 28.51
## Residual 2348.7 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 357.176 8.039 44.43
## I(scale(visitNum_centered)) 1.923 1.152 1.67
## trt2Weighted first -9.867 9.950 -0.99
## I(scale(IT)) -4.945 5.478 -0.90
## treatmentWeighted 2.153 2.113 1.02
## hive4 -4.947 10.573 -0.47
## I(scale(IT)^2) -5.289 3.917 -1.35
## I(scale(IT)):treatmentWeighted 3.785 2.202 1.72
##
## Correlation of Fixed Effects:
## (Intr) I((N_) trt2Wf I(s(IT)) trtmnW hive4 I((IT)^
## I(scl(vN_)) 0.043
## trt2Wghtdfr -0.502 0.024
## I(scal(IT)) -0.066 0.040 0.152
## trtmntWghtd -0.144 -0.214 0.006 -0.039
## hive4 -0.419 -0.013 -0.018 -0.005 0.002
## I(sc(IT)^2) -0.405 -0.017 -0.070 0.127 -0.015 0.060
## I(sc(IT)):W -0.014 -0.253 -0.007 -0.239 0.111 0.005 -0.034m2 <- update(m1.1, .~. - hive)
anova(m1.1, m2) # keep m2 (based on BIC)## Data: newdf3
## Models:
## m2: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m2: I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## m1.1: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m1.1: hive + I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m2 9 25146 25198 -12564 25128
## m1.1 10 25148 25205 -12564 25128 0.2182 1 0.6404summary(m2)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25145.9 25197.8 -12564.0 25127.9 2351
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2954 -0.4655 0.2005 0.6868 2.3943
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 818 28.60
## Residual 2349 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 355.602 7.323 48.56
## I(scale(visitNum_centered)) 1.916 1.152 1.66
## trt2Weighted first -9.951 9.979 -1.00
## I(scale(IT)) -4.957 5.494 -0.90
## treatmentWeighted 2.154 2.113 1.02
## I(scale(IT)^2) -5.179 3.922 -1.32
## I(scale(IT)):treatmentWeighted 3.791 2.202 1.72
##
## Correlation of Fixed Effects:
## (Intr) I((N_) trt2Wf I(s(IT)) trtmnW I((IT)^
## I(scl(vN_)) 0.041
## trt2Wghtdfr -0.561 0.023
## I(scal(IT)) -0.074 0.040 0.152
## trtmntWghtd -0.158 -0.214 0.006 -0.039
## I(sc(IT)^2) -0.419 -0.016 -0.069 0.127 -0.015
## I(sc(IT)):W -0.013 -0.253 -0.007 -0.238 0.111 -0.034m3 <- update(m2, .~. - I(scale(IT)^2))
anova(m2, m3) # keep m3## Data: newdf3
## Models:
## m3: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m3: (1 | beeID) + I(scale(IT)):treatment
## m2: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m2: I(scale(IT)^2) + (1 | beeID) + I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m3 8 25146 25192 -12565 25130
## m2 9 25146 25198 -12564 25128 1.7007 1 0.1922summary(m3)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## (1 | beeID) + I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25145.6 25191.8 -12564.8 25129.6 2352
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2974 -0.4648 0.1939 0.6878 2.3993
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 860.5 29.33
## Residual 2348.7 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 351.549 6.806 51.65
## I(scale(visitNum_centered)) 1.895 1.152 1.65
## trt2Weighted first -10.862 10.199 -1.06
## I(scale(IT)) -4.037 5.576 -0.72
## treatmentWeighted 2.113 2.113 1.00
## I(scale(IT)):treatmentWeighted 3.701 2.201 1.68
##
## Correlation of Fixed Effects:
## (Intr) I((N_) trt2Wf I(s(IT)) trtmnW
## I(scl(vN_)) 0.038
## trt2Wghtdfr -0.652 0.022
## I(scal(IT)) -0.024 0.041 0.162
## trtmntWghtd -0.176 -0.214 0.004 -0.036
## I(sc(IT)):W -0.029 -0.254 -0.009 -0.230 0.110m3.1 <- update(m3, .~. - trt2)
anova(m3, m3.1) # keep m3.1## Data: newdf3
## Models:
## m3.1: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + treatment +
## m3.1: (1 | beeID) + I(scale(IT)):treatment
## m3: freq ~ I(scale(visitNum_centered)) + trt2 + I(scale(IT)) + treatment +
## m3: (1 | beeID) + I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m3.1 7 25145 25185 -12565 25131
## m3 8 25146 25192 -12565 25130 1.1172 1 0.2905summary(m3.1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + treatment +
## (1 | beeID) + I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25144.8 25185.1 -12565.4 25130.8 2353
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3023 -0.4645 0.1920 0.6862 2.3959
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 888.4 29.81
## Residual 2348.7 48.46
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 346.822 5.236 66.24
## I(scale(visitNum_centered)) 1.922 1.152 1.67
## I(scale(IT)) -3.075 5.583 -0.55
## treatmentWeighted 2.123 2.113 1.00
## I(scale(IT)):treatmentWeighted 3.686 2.201 1.68
##
## Correlation of Fixed Effects:
## (Intr) I((N_) I(s(IT)) trtmnW
## I(scl(vN_)) 0.067
## I(scal(IT)) 0.109 0.038
## trtmntWghtd -0.226 -0.215 -0.037
## I(sc(IT)):W -0.046 -0.254 -0.228 0.111m4 <- update(m3.1, .~. - treatment)
anova(m3.1, m4) #keep m4## Data: newdf3
## Models:
## m4: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID) +
## m4: I(scale(IT)):treatment
## m3.1: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + treatment +
## m3.1: (1 | beeID) + I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m4 6 25144 25178 -12566 25132
## m3.1 7 25145 25185 -12565 25131 1.0089 1 0.3152summary(m4)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID) +
## I(scale(IT)):treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25143.8 25178.4 -12565.9 25131.8 2354
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2783 -0.4565 0.1932 0.6827 2.4222
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 888.5 29.81
## Residual 2349.7 48.47
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.008 5.102 68.22
## I(scale(visitNum_centered)) 2.171 1.125 1.93
## I(scale(IT)) -2.868 5.580 -0.51
## I(scale(IT)):treatmentWeighted 3.442 2.188 1.57
##
## Correlation of Fixed Effects:
## (Intr) I((N_) I(s(IT))
## I(scl(vN_)) 0.020
## I(scal(IT)) 0.104 0.031
## I(sc(IT)):W -0.022 -0.237 -0.226m5 <- update(m4, .~. -I(scale(IT)):treatment)
anova(m4, m5) # keep m5 -- baesd on BIC (agrees with GAMM analysis above)## Data: newdf3
## Models:
## m5: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID)
## m4: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID) +
## m4: I(scale(IT)):treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m5 5 25144 25173 -12567 25134
## m4 6 25144 25178 -12566 25132 2.4726 1 0.1158summary(m5)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID)
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25144.2 25173.1 -12567.1 25134.2 2355
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3038 -0.4736 0.1929 0.6902 2.3985
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 880.5 29.67
## Residual 2352.5 48.50
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.1844 5.0783 68.56
## I(scale(visitNum_centered)) 2.5898 1.0937 2.37
## I(scale(IT)) -0.8855 5.4117 -0.16
##
## Correlation of Fixed Effects:
## (Intr) I((N_)
## I(scl(vN_)) 0.015
## I(scal(IT)) 0.102 -0.024m6 <- update(m5, .~. - I(scale(IT)))
anova(m5, m6)## Data: newdf3
## Models:
## m6: freq ~ I(scale(visitNum_centered)) + (1 | beeID)
## m5: freq ~ I(scale(visitNum_centered)) + I(scale(IT)) + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m6 4 25142 25165 -12567 25134
## m5 5 25144 25173 -12567 25134 0.0268 1 0.8701summary(m6) ## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: freq ~ I(scale(visitNum_centered)) + (1 | beeID)
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25142.3 25165.3 -12567.1 25134.3 2356
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3033 -0.4735 0.1920 0.6906 2.3989
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 881.3 29.69
## Residual 2352.5 48.50
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.269 5.054 68.91
## I(scale(visitNum_centered)) 2.586 1.093 2.36
##
## Correlation of Fixed Effects:
## (Intr)
## I(scl(vN_)) 0.018m7 <- update(m6, .~. - I(scale(visitNum_centered)))
anova(m6, m7) # keep m7## Data: newdf3
## Models:
## m7: freq ~ (1 | beeID)
## m6: freq ~ I(scale(visitNum_centered)) + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m7 3 25146 25163 -12570 25140
## m6 4 25142 25165 -12567 25134 5.584 1 0.01813 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(m7)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: freq ~ (1 | beeID)
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 25145.8 25163.1 -12569.9 25139.8 2357
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3391 -0.4568 0.1808 0.6925 2.3602
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 875.4 29.59
## Residual 2358.4 48.56
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.056 5.037 69.09# get p-value for treament for paper
m_trt <- update(m7, .~. + treatment)
anova(m7, m_trt) # p-val for paper## Data: newdf3
## Models:
## m7: freq ~ (1 | beeID)
## m_trt: freq ~ (1 | beeID) + treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m7 3 25146 25163 -12570 25140
## m_trt 4 25146 25169 -12569 25138 1.5992 1 0.206m_IT <- update(m7, .~. + IT)
anova(m7, m_IT) # p-val for IT span## Data: newdf3
## Models:
## m7: freq ~ (1 | beeID)
## m_IT: freq ~ (1 | beeID) + IT
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m7 3 25146 25163 -12570 25140
## m_IT 4 25148 25171 -12570 25140 0.0114 1 0.9151# final freq mod for paper
finmod <- update(m7, .~., REML = TRUE)
summary(finmod) # final model for paper -- same as gamm## Linear mixed model fit by REML ['lmerMod']
## Formula: freq ~ (1 | beeID)
## Data: newdf3
##
## REML criterion at convergence: 25134.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3401 -0.4580 0.1806 0.6919 2.3616
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 901.6 30.03
## Residual 2358.4 48.56
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.056 5.109 68.12summary(finmod) # summary for paper -- no predictors predict frequency (when accounting for beeID)## Linear mixed model fit by REML ['lmerMod']
## Formula: freq ~ (1 | beeID)
## Data: newdf3
##
## REML criterion at convergence: 25134.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3401 -0.4580 0.1806 0.6919 2.3616
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 901.6 30.03
## Residual 2358.4 48.56
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 348.056 5.109 68.12plot(finmod)
qqnorm(ranef(finmod)$beeID[[1]])
qqline(ranef(finmod)$beeID[[1]])
sjp.lmer(finmod, type = "re", sort = TRUE) # plot random effects to find any outliers## Plotting random effects...
# sjp.lmer(finmod, type = 'fe', sort = TRUE, p.kr = FALSE) # plot fixed effectsBootstrap CI’s for figure for paper
# set number of bootstrap replicates for models
nbootSims = 10000
table(new_df$hive) # more trials from hive 3##
## 3 4
## 1644 716# using hive 3, since it's the one with the most data
# however, hive doesn't affect model anyway
# calculate an average IT for prediction
ITmean = mean(tapply(new_df$IT, INDEX = new_df$beeID, FUN = function(x) x[1] ))
pframe <- expand.grid(trt2 = levels(droplevels(newdf3$trt2)),
IT = ITmean,
visitNum_centered = -50:50,
hive = factor(3, levels = levels(newdf3$hive)),
beeID = 99999,
treatment = levels(newdf3$treatment))
pframe$freq <- 0
pframe <- pframe[(pframe$trt2 == "Sham first" &
pframe$treatment == "Sham" &
pframe$visitNum_centered < 0) |
(pframe$trt2 == "Sham first" &
pframe$treatment == "Weighted" &
pframe$visitNum_centered > 0) |
(pframe$trt2 == "Weighted first" &
pframe$treatment == "Weighted" &
pframe$visitNum_centered < 0) |
(pframe$trt2 == "Weighted first" &
pframe$treatment == "Sham" &
pframe$visitNum_centered > 0)
, ]
# make a model to show the effect of treatment in a plot
m1 <- update(finmod, .~. + treatment)
pp <- predict(m1, newdata = pframe, re.form=NA, type = 'response') # re.form sets all random effects to 0
### Calculate CI's (using bootstrap, not accounting for random effects)
bb2 <- bootMer(m1, FUN=function(x) predict(x, pframe, re.form=NA, type = 'response'), nsim = nbootSims)## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce q
## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce q
## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce q
## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce q
## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce qprint(paste("Number of bootstrap samples", nrow(bb2$t)))## [1] "Number of bootstrap samples 10000"bb2_se <-apply(bb2$t,2,function(x) quantile(x, probs = c(0.025, 0.975)))
pframe$blo<-bb2_se[1,]
pframe$bhi<-bb2_se[2,]
pframe$predMean <- pp
pframe## trt2 IT visitNum_centered hive beeID treatment freq
## 1 Sham first 3.965833 -50 3 99999 Sham 0
## 3 Sham first 3.965833 -49 3 99999 Sham 0
## 5 Sham first 3.965833 -48 3 99999 Sham 0
## 7 Sham first 3.965833 -47 3 99999 Sham 0
## 9 Sham first 3.965833 -46 3 99999 Sham 0
## 11 Sham first 3.965833 -45 3 99999 Sham 0
## 13 Sham first 3.965833 -44 3 99999 Sham 0
## 15 Sham first 3.965833 -43 3 99999 Sham 0
## 17 Sham first 3.965833 -42 3 99999 Sham 0
## 19 Sham first 3.965833 -41 3 99999 Sham 0
## 21 Sham first 3.965833 -40 3 99999 Sham 0
## 23 Sham first 3.965833 -39 3 99999 Sham 0
## 25 Sham first 3.965833 -38 3 99999 Sham 0
## 27 Sham first 3.965833 -37 3 99999 Sham 0
## 29 Sham first 3.965833 -36 3 99999 Sham 0
## 31 Sham first 3.965833 -35 3 99999 Sham 0
## 33 Sham first 3.965833 -34 3 99999 Sham 0
## 35 Sham first 3.965833 -33 3 99999 Sham 0
## 37 Sham first 3.965833 -32 3 99999 Sham 0
## 39 Sham first 3.965833 -31 3 99999 Sham 0
## 41 Sham first 3.965833 -30 3 99999 Sham 0
## 43 Sham first 3.965833 -29 3 99999 Sham 0
## 45 Sham first 3.965833 -28 3 99999 Sham 0
## 47 Sham first 3.965833 -27 3 99999 Sham 0
## 49 Sham first 3.965833 -26 3 99999 Sham 0
## 51 Sham first 3.965833 -25 3 99999 Sham 0
## 53 Sham first 3.965833 -24 3 99999 Sham 0
## 55 Sham first 3.965833 -23 3 99999 Sham 0
## 57 Sham first 3.965833 -22 3 99999 Sham 0
## 59 Sham first 3.965833 -21 3 99999 Sham 0
## 61 Sham first 3.965833 -20 3 99999 Sham 0
## 63 Sham first 3.965833 -19 3 99999 Sham 0
## 65 Sham first 3.965833 -18 3 99999 Sham 0
## 67 Sham first 3.965833 -17 3 99999 Sham 0
## 69 Sham first 3.965833 -16 3 99999 Sham 0
## 71 Sham first 3.965833 -15 3 99999 Sham 0
## 73 Sham first 3.965833 -14 3 99999 Sham 0
## 75 Sham first 3.965833 -13 3 99999 Sham 0
## 77 Sham first 3.965833 -12 3 99999 Sham 0
## 79 Sham first 3.965833 -11 3 99999 Sham 0
## 81 Sham first 3.965833 -10 3 99999 Sham 0
## 83 Sham first 3.965833 -9 3 99999 Sham 0
## 85 Sham first 3.965833 -8 3 99999 Sham 0
## 87 Sham first 3.965833 -7 3 99999 Sham 0
## 89 Sham first 3.965833 -6 3 99999 Sham 0
## 91 Sham first 3.965833 -5 3 99999 Sham 0
## 93 Sham first 3.965833 -4 3 99999 Sham 0
## 95 Sham first 3.965833 -3 3 99999 Sham 0
## 97 Sham first 3.965833 -2 3 99999 Sham 0
## 99 Sham first 3.965833 -1 3 99999 Sham 0
## 104 Weighted first 3.965833 1 3 99999 Sham 0
## 106 Weighted first 3.965833 2 3 99999 Sham 0
## 108 Weighted first 3.965833 3 3 99999 Sham 0
## 110 Weighted first 3.965833 4 3 99999 Sham 0
## 112 Weighted first 3.965833 5 3 99999 Sham 0
## 114 Weighted first 3.965833 6 3 99999 Sham 0
## 116 Weighted first 3.965833 7 3 99999 Sham 0
## 118 Weighted first 3.965833 8 3 99999 Sham 0
## 120 Weighted first 3.965833 9 3 99999 Sham 0
## 122 Weighted first 3.965833 10 3 99999 Sham 0
## 124 Weighted first 3.965833 11 3 99999 Sham 0
## 126 Weighted first 3.965833 12 3 99999 Sham 0
## 128 Weighted first 3.965833 13 3 99999 Sham 0
## 130 Weighted first 3.965833 14 3 99999 Sham 0
## 132 Weighted first 3.965833 15 3 99999 Sham 0
## 134 Weighted first 3.965833 16 3 99999 Sham 0
## 136 Weighted first 3.965833 17 3 99999 Sham 0
## 138 Weighted first 3.965833 18 3 99999 Sham 0
## 140 Weighted first 3.965833 19 3 99999 Sham 0
## 142 Weighted first 3.965833 20 3 99999 Sham 0
## 144 Weighted first 3.965833 21 3 99999 Sham 0
## 146 Weighted first 3.965833 22 3 99999 Sham 0
## 148 Weighted first 3.965833 23 3 99999 Sham 0
## 150 Weighted first 3.965833 24 3 99999 Sham 0
## 152 Weighted first 3.965833 25 3 99999 Sham 0
## 154 Weighted first 3.965833 26 3 99999 Sham 0
## 156 Weighted first 3.965833 27 3 99999 Sham 0
## 158 Weighted first 3.965833 28 3 99999 Sham 0
## 160 Weighted first 3.965833 29 3 99999 Sham 0
## 162 Weighted first 3.965833 30 3 99999 Sham 0
## 164 Weighted first 3.965833 31 3 99999 Sham 0
## 166 Weighted first 3.965833 32 3 99999 Sham 0
## 168 Weighted first 3.965833 33 3 99999 Sham 0
## 170 Weighted first 3.965833 34 3 99999 Sham 0
## 172 Weighted first 3.965833 35 3 99999 Sham 0
## 174 Weighted first 3.965833 36 3 99999 Sham 0
## 176 Weighted first 3.965833 37 3 99999 Sham 0
## 178 Weighted first 3.965833 38 3 99999 Sham 0
## 180 Weighted first 3.965833 39 3 99999 Sham 0
## 182 Weighted first 3.965833 40 3 99999 Sham 0
## 184 Weighted first 3.965833 41 3 99999 Sham 0
## 186 Weighted first 3.965833 42 3 99999 Sham 0
## 188 Weighted first 3.965833 43 3 99999 Sham 0
## 190 Weighted first 3.965833 44 3 99999 Sham 0
## 192 Weighted first 3.965833 45 3 99999 Sham 0
## 194 Weighted first 3.965833 46 3 99999 Sham 0
## 196 Weighted first 3.965833 47 3 99999 Sham 0
## 198 Weighted first 3.965833 48 3 99999 Sham 0
## 200 Weighted first 3.965833 49 3 99999 Sham 0
## 202 Weighted first 3.965833 50 3 99999 Sham 0
## 204 Weighted first 3.965833 -50 3 99999 Weighted 0
## 206 Weighted first 3.965833 -49 3 99999 Weighted 0
## 208 Weighted first 3.965833 -48 3 99999 Weighted 0
## 210 Weighted first 3.965833 -47 3 99999 Weighted 0
## 212 Weighted first 3.965833 -46 3 99999 Weighted 0
## 214 Weighted first 3.965833 -45 3 99999 Weighted 0
## 216 Weighted first 3.965833 -44 3 99999 Weighted 0
## 218 Weighted first 3.965833 -43 3 99999 Weighted 0
## 220 Weighted first 3.965833 -42 3 99999 Weighted 0
## 222 Weighted first 3.965833 -41 3 99999 Weighted 0
## 224 Weighted first 3.965833 -40 3 99999 Weighted 0
## 226 Weighted first 3.965833 -39 3 99999 Weighted 0
## 228 Weighted first 3.965833 -38 3 99999 Weighted 0
## 230 Weighted first 3.965833 -37 3 99999 Weighted 0
## 232 Weighted first 3.965833 -36 3 99999 Weighted 0
## 234 Weighted first 3.965833 -35 3 99999 Weighted 0
## 236 Weighted first 3.965833 -34 3 99999 Weighted 0
## 238 Weighted first 3.965833 -33 3 99999 Weighted 0
## 240 Weighted first 3.965833 -32 3 99999 Weighted 0
## 242 Weighted first 3.965833 -31 3 99999 Weighted 0
## 244 Weighted first 3.965833 -30 3 99999 Weighted 0
## 246 Weighted first 3.965833 -29 3 99999 Weighted 0
## 248 Weighted first 3.965833 -28 3 99999 Weighted 0
## 250 Weighted first 3.965833 -27 3 99999 Weighted 0
## 252 Weighted first 3.965833 -26 3 99999 Weighted 0
## 254 Weighted first 3.965833 -25 3 99999 Weighted 0
## 256 Weighted first 3.965833 -24 3 99999 Weighted 0
## 258 Weighted first 3.965833 -23 3 99999 Weighted 0
## 260 Weighted first 3.965833 -22 3 99999 Weighted 0
## 262 Weighted first 3.965833 -21 3 99999 Weighted 0
## 264 Weighted first 3.965833 -20 3 99999 Weighted 0
## 266 Weighted first 3.965833 -19 3 99999 Weighted 0
## 268 Weighted first 3.965833 -18 3 99999 Weighted 0
## 270 Weighted first 3.965833 -17 3 99999 Weighted 0
## 272 Weighted first 3.965833 -16 3 99999 Weighted 0
## 274 Weighted first 3.965833 -15 3 99999 Weighted 0
## 276 Weighted first 3.965833 -14 3 99999 Weighted 0
## 278 Weighted first 3.965833 -13 3 99999 Weighted 0
## 280 Weighted first 3.965833 -12 3 99999 Weighted 0
## 282 Weighted first 3.965833 -11 3 99999 Weighted 0
## 284 Weighted first 3.965833 -10 3 99999 Weighted 0
## 286 Weighted first 3.965833 -9 3 99999 Weighted 0
## 288 Weighted first 3.965833 -8 3 99999 Weighted 0
## 290 Weighted first 3.965833 -7 3 99999 Weighted 0
## 292 Weighted first 3.965833 -6 3 99999 Weighted 0
## 294 Weighted first 3.965833 -5 3 99999 Weighted 0
## 296 Weighted first 3.965833 -4 3 99999 Weighted 0
## 298 Weighted first 3.965833 -3 3 99999 Weighted 0
## 300 Weighted first 3.965833 -2 3 99999 Weighted 0
## 302 Weighted first 3.965833 -1 3 99999 Weighted 0
## 305 Sham first 3.965833 1 3 99999 Weighted 0
## 307 Sham first 3.965833 2 3 99999 Weighted 0
## 309 Sham first 3.965833 3 3 99999 Weighted 0
## 311 Sham first 3.965833 4 3 99999 Weighted 0
## 313 Sham first 3.965833 5 3 99999 Weighted 0
## 315 Sham first 3.965833 6 3 99999 Weighted 0
## 317 Sham first 3.965833 7 3 99999 Weighted 0
## 319 Sham first 3.965833 8 3 99999 Weighted 0
## 321 Sham first 3.965833 9 3 99999 Weighted 0
## 323 Sham first 3.965833 10 3 99999 Weighted 0
## 325 Sham first 3.965833 11 3 99999 Weighted 0
## 327 Sham first 3.965833 12 3 99999 Weighted 0
## 329 Sham first 3.965833 13 3 99999 Weighted 0
## 331 Sham first 3.965833 14 3 99999 Weighted 0
## 333 Sham first 3.965833 15 3 99999 Weighted 0
## 335 Sham first 3.965833 16 3 99999 Weighted 0
## 337 Sham first 3.965833 17 3 99999 Weighted 0
## 339 Sham first 3.965833 18 3 99999 Weighted 0
## 341 Sham first 3.965833 19 3 99999 Weighted 0
## 343 Sham first 3.965833 20 3 99999 Weighted 0
## 345 Sham first 3.965833 21 3 99999 Weighted 0
## 347 Sham first 3.965833 22 3 99999 Weighted 0
## 349 Sham first 3.965833 23 3 99999 Weighted 0
## 351 Sham first 3.965833 24 3 99999 Weighted 0
## 353 Sham first 3.965833 25 3 99999 Weighted 0
## 355 Sham first 3.965833 26 3 99999 Weighted 0
## 357 Sham first 3.965833 27 3 99999 Weighted 0
## 359 Sham first 3.965833 28 3 99999 Weighted 0
## 361 Sham first 3.965833 29 3 99999 Weighted 0
## 363 Sham first 3.965833 30 3 99999 Weighted 0
## 365 Sham first 3.965833 31 3 99999 Weighted 0
## 367 Sham first 3.965833 32 3 99999 Weighted 0
## 369 Sham first 3.965833 33 3 99999 Weighted 0
## 371 Sham first 3.965833 34 3 99999 Weighted 0
## 373 Sham first 3.965833 35 3 99999 Weighted 0
## 375 Sham first 3.965833 36 3 99999 Weighted 0
## 377 Sham first 3.965833 37 3 99999 Weighted 0
## 379 Sham first 3.965833 38 3 99999 Weighted 0
## 381 Sham first 3.965833 39 3 99999 Weighted 0
## 383 Sham first 3.965833 40 3 99999 Weighted 0
## 385 Sham first 3.965833 41 3 99999 Weighted 0
## 387 Sham first 3.965833 42 3 99999 Weighted 0
## 389 Sham first 3.965833 43 3 99999 Weighted 0
## 391 Sham first 3.965833 44 3 99999 Weighted 0
## 393 Sham first 3.965833 45 3 99999 Weighted 0
## 395 Sham first 3.965833 46 3 99999 Weighted 0
## 397 Sham first 3.965833 47 3 99999 Weighted 0
## 399 Sham first 3.965833 48 3 99999 Weighted 0
## 401 Sham first 3.965833 49 3 99999 Weighted 0
## 403 Sham first 3.965833 50 3 99999 Weighted 0
## blo bhi predMean
## 1 336.4795 356.5832 346.6421
## 3 336.4795 356.5832 346.6421
## 5 336.4795 356.5832 346.6421
## 7 336.4795 356.5832 346.6421
## 9 336.4795 356.5832 346.6421
## 11 336.4795 356.5832 346.6421
## 13 336.4795 356.5832 346.6421
## 15 336.4795 356.5832 346.6421
## 17 336.4795 356.5832 346.6421
## 19 336.4795 356.5832 346.6421
## 21 336.4795 356.5832 346.6421
## 23 336.4795 356.5832 346.6421
## 25 336.4795 356.5832 346.6421
## 27 336.4795 356.5832 346.6421
## 29 336.4795 356.5832 346.6421
## 31 336.4795 356.5832 346.6421
## 33 336.4795 356.5832 346.6421
## 35 336.4795 356.5832 346.6421
## 37 336.4795 356.5832 346.6421
## 39 336.4795 356.5832 346.6421
## 41 336.4795 356.5832 346.6421
## 43 336.4795 356.5832 346.6421
## 45 336.4795 356.5832 346.6421
## 47 336.4795 356.5832 346.6421
## 49 336.4795 356.5832 346.6421
## 51 336.4795 356.5832 346.6421
## 53 336.4795 356.5832 346.6421
## 55 336.4795 356.5832 346.6421
## 57 336.4795 356.5832 346.6421
## 59 336.4795 356.5832 346.6421
## 61 336.4795 356.5832 346.6421
## 63 336.4795 356.5832 346.6421
## 65 336.4795 356.5832 346.6421
## 67 336.4795 356.5832 346.6421
## 69 336.4795 356.5832 346.6421
## 71 336.4795 356.5832 346.6421
## 73 336.4795 356.5832 346.6421
## 75 336.4795 356.5832 346.6421
## 77 336.4795 356.5832 346.6421
## 79 336.4795 356.5832 346.6421
## 81 336.4795 356.5832 346.6421
## 83 336.4795 356.5832 346.6421
## 85 336.4795 356.5832 346.6421
## 87 336.4795 356.5832 346.6421
## 89 336.4795 356.5832 346.6421
## 91 336.4795 356.5832 346.6421
## 93 336.4795 356.5832 346.6421
## 95 336.4795 356.5832 346.6421
## 97 336.4795 356.5832 346.6421
## 99 336.4795 356.5832 346.6421
## 104 336.4795 356.5832 346.6421
## 106 336.4795 356.5832 346.6421
## 108 336.4795 356.5832 346.6421
## 110 336.4795 356.5832 346.6421
## 112 336.4795 356.5832 346.6421
## 114 336.4795 356.5832 346.6421
## 116 336.4795 356.5832 346.6421
## 118 336.4795 356.5832 346.6421
## 120 336.4795 356.5832 346.6421
## 122 336.4795 356.5832 346.6421
## 124 336.4795 356.5832 346.6421
## 126 336.4795 356.5832 346.6421
## 128 336.4795 356.5832 346.6421
## 130 336.4795 356.5832 346.6421
## 132 336.4795 356.5832 346.6421
## 134 336.4795 356.5832 346.6421
## 136 336.4795 356.5832 346.6421
## 138 336.4795 356.5832 346.6421
## 140 336.4795 356.5832 346.6421
## 142 336.4795 356.5832 346.6421
## 144 336.4795 356.5832 346.6421
## 146 336.4795 356.5832 346.6421
## 148 336.4795 356.5832 346.6421
## 150 336.4795 356.5832 346.6421
## 152 336.4795 356.5832 346.6421
## 154 336.4795 356.5832 346.6421
## 156 336.4795 356.5832 346.6421
## 158 336.4795 356.5832 346.6421
## 160 336.4795 356.5832 346.6421
## 162 336.4795 356.5832 346.6421
## 164 336.4795 356.5832 346.6421
## 166 336.4795 356.5832 346.6421
## 168 336.4795 356.5832 346.6421
## 170 336.4795 356.5832 346.6421
## 172 336.4795 356.5832 346.6421
## 174 336.4795 356.5832 346.6421
## 176 336.4795 356.5832 346.6421
## 178 336.4795 356.5832 346.6421
## 180 336.4795 356.5832 346.6421
## 182 336.4795 356.5832 346.6421
## 184 336.4795 356.5832 346.6421
## 186 336.4795 356.5832 346.6421
## 188 336.4795 356.5832 346.6421
## 190 336.4795 356.5832 346.6421
## 192 336.4795 356.5832 346.6421
## 194 336.4795 356.5832 346.6421
## 196 336.4795 356.5832 346.6421
## 198 336.4795 356.5832 346.6421
## 200 336.4795 356.5832 346.6421
## 202 336.4795 356.5832 346.6421
## 204 339.0374 359.2846 349.2520
## 206 339.0374 359.2846 349.2520
## 208 339.0374 359.2846 349.2520
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## 403 339.0374 359.2846 349.2520### Make frequency plots for paper
# predictions are from this model
summary(m1)## Linear mixed model fit by REML ['lmerMod']
## Formula: freq ~ (1 | beeID) + treatment
## Data: newdf3
##
## REML criterion at convergence: 25129.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3673 -0.4740 0.1874 0.6837 2.3307
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 901.5 30.02
## Residual 2357.8 48.56
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 346.642 5.230 66.28
## treatmentWeighted 2.610 2.064 1.26
##
## Correlation of Fixed Effects:
## (Intr)
## trtmntWghtd -0.214anova(m1, update(m1, .~. - treatment)) #p-val and BIC for paper## refitting model(s) with ML (instead of REML)## Data: newdf3
## Models:
## update(m1, . ~ . - treatment): freq ~ (1 | beeID)
## m1: freq ~ (1 | beeID) + treatment
## Df AIC BIC logLik deviance Chisq Chi Df
## update(m1, . ~ . - treatment) 3 25146 25163 -12570 25140
## m1 4 25146 25169 -12569 25138 1.5992 1
## Pr(>Chisq)
## update(m1, . ~ . - treatment)
## m1 0.206pframe$trt3 <- mapvalues(pframe$trt2, from = c("Sham first", "Weighted first"),
to = c("Sham -> Weighted", "Weighted -> Sham"))
g0 <- ggplot(pframe, aes(x=visitNum_centered, y=predMean))+
geom_line(aes(color = treatment))+
labs(y = "Sonication frequency (Hz)", x = "Sonication number\n (0 is when treatment switched)") +
geom_ribbon(aes(x = visitNum_centered, ymin = blo, ymax = bhi, fill= treatment), alpha = 0.2) +
facet_wrap(~trt3) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
scale_fill_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = c(0.5, 0.90),
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal") +
ylim(c(330, 370))
g0
ggsave(filename = file.path(figDir, "WeightedSham_Freq_Timeseries.pdf"), width =5, height = 3.6)
g1 <- g0 + geom_point(data = newdf3[newdf3$visitNum_centered < 50,],
aes(x = visitNum_centered, y = freq), position = position_jitter(height = 5), size = 0.1, pch = 16, alpha = 0.4) +
ylim(c(220, 470))## Scale for 'y' is already present. Adding another scale for 'y', which
## will replace the existing scale.g1 # note that the distribution of frequency is a bit bimodal -- this could be 
# a problem, so we ran the analysis with a freq cutoff at 270
# we found no significant differences in the models either way.
ggsave(filename = file.path(figDir, "WeightedSham_Freq_Timeseries_RawData.pdf"), width =5, height = 3.6)
g1 <- g0 + geom_point(data = newdf3[newdf3$visitNum_centered < 50,],
aes(x = visitNum_centered, y = freq), position = position_jitter(height = 5), size = 0.1, pch = 16, alpha = 0.4) +
ylim(c(270, 480))## Scale for 'y' is already present. Adding another scale for 'y', which
## will replace the existing scale.g1## Warning: Removed 741 rows containing missing values (geom_point).
ggsave(filename = file.path(figDir, "WeightedSham_Freq_Timeseries_RawData_trimmed.pdf"), width =5, height = 3.6)## Warning: Removed 733 rows containing missing values (geom_point).# mean and 95% CI (without visit number)
g0_freq <- ggplot(pframe[pframe$visitNum_centered %in% c(-25, 25), ], aes(x=treatment, y=predMean))+
geom_point(aes(color = treatment), alpha = 1) +
labs(y = "Sonication frequency (Hz)", x = "Flower treatment") +
geom_errorbar(aes(x = treatment, ymin = blo, ymax = bhi, color= treatment), alpha = 1, width = 0.1) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0, end = 0, option = "A") +
theme(legend.position = "none",
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0_freq
ggsave(filename = file.path(figDir, "WeightedSham_Freq_pointWhiskers_BW.pdf"), width =2.5, height = 3)
g0 <- ggplot(pframe[pframe$visitNum_centered %in% c(-25, 25), ], aes(x=treatment, y=predMean))+
geom_point(aes(color = treatment), alpha = 1) +
labs(y = "Sonication frequency (Hz)", x = "Flower treatment") +
geom_errorbar(aes(x = treatment, ymin = blo, ymax = bhi, color= treatment), alpha = 1, width = 0.1) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = "none",
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0
ggsave(filename = file.path(figDir, "WeightedSham_Freq_pointWhiskers.pdf"), width =5, height = 3.6)
Fig2a <- g0
## add raw data
g1 <- g0 + geom_point(data = newdf3, aes(x = treatment, y = freq, color = treatment), position = position_jitter(width = 0.1, height = 6), alpha = 0.4, pch = 16, size = 0.2)
g1
ggsave(filename = file.path(figDir, "WeightedSham_Freq_pointWhiskers_rawData.pdf"), width =5, height = 3.6)
# "Mean and bootstrap CI based on fixed-effects uncertainty ONLY"
g0 <- ggplot(pframe, aes(x=visitNum_centered, y=predMean))+
geom_point()+
labs(y = "Sonication frequency (Hz)", x = "buzzNumber") +
geom_ribbon(aes(x = visitNum_centered, ymin = blo, ymax = bhi), alpha = 0.2) +
facet_wrap(~trt2)
g0
# plot effect to see if it agrees
plot(Effect(c("treatment"), m1))
Modeling amplitude with gamm
g01 = gamm4(log(amp_acc) ~ s(visitNum_centered, by = trt2) + trt2 + IT + hive + treatment, random = ~(1|beeID), data = newdf3)
par(mfrow = c(2,3))
aab <- plot(g01$gam, all.terms = TRUE, rug = FALSE, shade = TRUE)
summary(g01$gam) # Summary for paper ##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(amp_acc) ~ s(visitNum_centered, by = trt2) + trt2 + IT +
## hive + treatment
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.03662 0.58219 3.498 0.000477 ***
## trt2Weighted first -0.05297 0.09833 -0.539 0.590179
## IT 0.21347 0.14365 1.486 0.137405
## hive4 0.09955 0.10391 0.958 0.338173
## treatmentWeighted -0.32857 0.04921 -6.678 3.02e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered):trt2Sham first 1.414 1.414 4.924 0.0175 *
## s(visitNum_centered):trt2Weighted first 2.800 2.800 3.683 0.0323 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0571
## lmer.REML = 4557.5 Scale est. = 0.384 n = 2360summary(g01$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4557.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9897 -0.5342 0.1125 0.6707 2.6828
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.076179 0.27601
## Xr.0 s(visitNum_centered):trt2Weighted first 0.376255 0.61340
## Xr s(visitNum_centered):trt2Sham first 0.008701 0.09328
## Residual 0.384002 0.61968
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 2.036625 0.582186 3.498
## Xtrt2Weighted first -0.052966 0.098331 -0.539
## XIT 0.213470 0.143651 1.486
## Xhive4 0.099547 0.103913 0.958
## XtreatmentWeighted -0.328574 0.049206 -6.678
## Xs(visitNum_centered):trt2Sham firstFx1 0.059922 0.036356 1.648
## Xs(visitNum_centered):trt2Weighted firstFx1 0.003639 0.188745 0.019
##
## Correlation of Fixed Effects:
## X(Int) Xtr2Wf XIT Xhive4 XtrtmW X(N_):2Sf
## Xtrt2Wghtdf -0.238
## XIT -0.991 0.166
## Xhive4 -0.041 -0.011 -0.012
## XtrtmntWght -0.062 0.061 0.015 0.000
## X(N_):2SfF1 0.051 -0.029 -0.030 -0.003 -0.455
## X(N_):2WfF1 -0.001 0.060 0.000 0.001 0.023 -0.011dev.off()## null device
## 1g011 = gamm4(log(amp_acc) ~ s(visitNum_centered, by = trt2) + IT + hive + treatment, random = ~(1|beeID), data = newdf3)
par(mfrow = c(2,3))
aab <- plot(g011$gam, all.terms = TRUE, rug = FALSE, shade = TRUE)
summary(g011$gam) ##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(amp_acc) ~ s(visitNum_centered, by = trt2) + IT + hive +
## treatment
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.96224 0.55974 3.506 0.000464 ***
## IT 0.22614 0.14023 1.613 0.106971
## hive4 0.09890 0.10286 0.961 0.336419
## treatmentWeighted -0.32629 0.04905 -6.652 3.58e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered):trt2Sham first 1.396 1.396 4.868 0.0185 *
## s(visitNum_centered):trt2Weighted first 2.824 2.824 3.711 0.0286 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0543
## lmer.REML = 4555 Scale est. = 0.38399 n = 2360summary(g011$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4555
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9904 -0.5310 0.1120 0.6721 2.6775
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.074527 0.27300
## Xr.0 s(visitNum_centered):trt2Weighted first 0.387227 0.62228
## Xr s(visitNum_centered):trt2Sham first 0.008222 0.09068
## Residual 0.383989 0.61967
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 1.96224 0.55974 3.506
## XIT 0.22614 0.14023 1.613
## Xhive4 0.09890 0.10286 0.961
## XtreatmentWeighted -0.32629 0.04905 -6.652
## Xs(visitNum_centered):trt2Sham firstFx1 0.05943 0.03583 1.659
## Xs(visitNum_centered):trt2Weighted firstFx1 0.01018 0.19078 0.053
##
## Correlation of Fixed Effects:
## X(Int) XIT Xhive4 XtrtmW X(N_):2Sf
## XIT -0.994
## Xhive4 -0.045 -0.011
## XtrtmntWght -0.049 0.005 0.001
## X(N_):2SfF1 0.046 -0.026 -0.003 -0.463
## X(N_):2WfF1 0.014 -0.010 0.002 0.018 -0.008dev.off()## null device
## 1anova(g01$mer, g011$mer) # go with g011## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g011$mer: NULL
## g01$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g011$mer 10 4553.4 4611.1 -2266.7 4533.4
## g01$mer 11 4555.1 4618.5 -2266.5 4533.1 0.3497 1 0.5543g02 = gamm4(log(amp_acc) ~ s(visitNum_centered, by = trt2) + IT + treatment, random = ~(1|beeID), data = newdf3)
par(mfrow = c(2,3))
aab <- plot(g02$gam, all.terms = TRUE, rug = FALSE, shade = TRUE)
summary(g02$gam) # Summary for paper ##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(amp_acc) ~ s(visitNum_centered, by = trt2) + IT + treatment
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.98646 0.55806 3.560 0.000379 ***
## IT 0.22770 0.13995 1.627 0.103864
## treatmentWeighted -0.32686 0.04912 -6.655 3.52e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered):trt2Sham first 1.412 1.412 4.868 0.0182 *
## s(visitNum_centered):trt2Weighted first 2.810 2.810 3.669 0.0310 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0534
## lmer.REML = 4553.2 Scale est. = 0.384 n = 2360summary(g02$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4553.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9949 -0.5328 0.1143 0.6739 2.6875
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.074211 0.27242
## Xr.0 s(visitNum_centered):trt2Weighted first 0.379483 0.61602
## Xr s(visitNum_centered):trt2Sham first 0.008663 0.09307
## Residual 0.384001 0.61968
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 1.986456 0.558065 3.560
## XIT 0.227704 0.139951 1.627
## XtreatmentWeighted -0.326857 0.049116 -6.655
## Xs(visitNum_centered):trt2Sham firstFx1 0.059463 0.036299 1.638
## Xs(visitNum_centered):trt2Weighted firstFx1 0.009651 0.189098 0.051
##
## Correlation of Fixed Effects:
## X(Int) XIT XtrtmW X(N_):2Sf
## XIT -0.995
## XtrtmntWght -0.049 0.005
## X(N_):2SfF1 0.046 -0.026 -0.455
## X(N_):2WfF1 0.014 -0.010 0.019 -0.009dev.off()## null device
## 1anova(g011$mer, g02$mer) # g02 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g02$mer: NULL
## g011$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g02$mer 9 4552.4 4604.3 -2267.2 4534.4
## g011$mer 10 4553.4 4611.1 -2266.7 4533.4 0.9778 1 0.3228g03 = gamm4(log(amp_acc) ~ s(visitNum_centered, by = trt2) + treatment, random = ~(1|beeID), data = newdf3)
anova(g02$mer, g03$mer) #keep g03## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g03$mer: NULL
## g02$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g03$mer 8 4553.1 4599.2 -2268.5 4537.1
## g02$mer 9 4552.4 4604.3 -2267.2 4534.4 2.691 1 0.1009summary(g03$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4553.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9839 -0.5287 0.1117 0.6716 2.6967
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.077961 0.27921
## Xr.0 s(visitNum_centered):trt2Weighted first 0.397557 0.63052
## Xr s(visitNum_centered):trt2Sham first 0.005922 0.07696
## Residual 0.384011 0.61969
## Number of obs: 2360, groups: beeID, 36; Xr.0, 8; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 2.88897 0.05438 53.12
## XtreatmentWeighted -0.32459 0.04854 -6.69
## Xs(visitNum_centered):trt2Sham firstFx1 0.06166 0.03320 1.86
## Xs(visitNum_centered):trt2Weighted firstFx1 0.01321 0.19301 0.07
##
## Correlation of Fixed Effects:
## X(Int) XtrtmW X(N_):2Sf
## XtrtmntWght -0.451
## X(N_):2SfF1 0.228 -0.510
## X(N_):2WfF1 0.040 0.017 -0.009g04 <- gamm4(log(amp_acc) ~ s(visitNum_centered) + treatment, random = ~(1|beeID), data = newdf3)
anova(g03$mer, g04$mer) #g04 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g04$mer: NULL
## g03$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g04$mer 6 4551.2 4585.8 -2269.6 4539.2
## g03$mer 8 4553.1 4599.2 -2268.5 4537.1 2.1425 2 0.3426summary(g04$gam) # approx p-value for smooth##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(amp_acc) ~ s(visitNum_centered) + treatment
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.87225 0.05047 56.91 <2e-16 ***
## treatmentWeighted -0.29794 0.02688 -11.08 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered) 2.056 2.056 6.862 0.00106 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0378
## lmer.REML = 4555.5 Scale est. = 0.38524 n = 2360summary(g04$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4555.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0433 -0.5427 0.1059 0.6832 2.7605
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07754 0.2785
## Xr s(visitNum_centered) 0.02027 0.1424
## Residual 0.38524 0.6207
## Number of obs: 2360, groups: beeID, 36; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 2.87225 0.05047 56.91
## XtreatmentWeighted -0.29794 0.02688 -11.08
## Xs(visitNum_centered)Fx1 0.02517 0.04290 0.59
##
## Correlation of Fixed Effects:
## X(Int) XtrtmW
## XtrtmntWght -0.293
## Xs(vstN_)F1 0.024 -0.053g44 <- gamm4(log(amp_acc) ~ visitNum_centered + treatment, random = ~(1|beeID), data = newdf3)
g05 <- gamm4(log(amp_acc) ~ treatment, random = ~(1|beeID), data = newdf3)
anova(g44$mer, g05$mer) #g44 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g05$mer: NULL
## g44$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g05$mer 4 4560.8 4583.9 -2276.4 4552.8
## g44$mer 5 4549.2 4578.0 -2269.6 4539.2 13.63 1 0.0002226 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1g06 <- gamm4(log(amp_acc) ~ visitNum_centered , random = ~(1|beeID), data = newdf3)
anova(g44$mer, g06$mer) #g044 better## refitting model(s) with ML (instead of REML)## Data: NULL
## Models:
## g06$mer: NULL
## g44$mer: NULL
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## g06$mer 4 4666.2 4689.3 -2329.1 4658.2
## g44$mer 5 4549.2 4578.0 -2269.6 4539.2 119.02 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# final model -- only treatment matters
ampMod <- g04
summary(ampMod$mer)## Linear mixed model fit by REML ['lmerMod']
##
## REML criterion at convergence: 4555.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0433 -0.5427 0.1059 0.6832 2.7605
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07754 0.2785
## Xr s(visitNum_centered) 0.02027 0.1424
## Residual 0.38524 0.6207
## Number of obs: 2360, groups: beeID, 36; Xr, 8
##
## Fixed effects:
## Estimate Std. Error t value
## X(Intercept) 2.87225 0.05047 56.91
## XtreatmentWeighted -0.29794 0.02688 -11.08
## Xs(visitNum_centered)Fx1 0.02517 0.04290 0.59
##
## Correlation of Fixed Effects:
## X(Int) XtrtmW
## XtrtmntWght -0.293
## Xs(vstN_)F1 0.024 -0.053summary(ampMod$gam)##
## Family: gaussian
## Link function: identity
##
## Formula:
## log(amp_acc) ~ s(visitNum_centered) + treatment
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.87225 0.05047 56.91 <2e-16 ***
## treatmentWeighted -0.29794 0.02688 -11.08 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(visitNum_centered) 2.056 2.056 6.862 0.00106 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0378
## lmer.REML = 4555.5 Scale est. = 0.38524 n = 2360plot(ampMod$mer)
par(mfrow = c(2,1))
plot(ampMod$gam, all.terms = TRUE, rug = FALSE, shade = TRUE)
dev.off()## null device
## 1Modeling amplitude with lmer
# log transform for acceleration helps model fit better
# start with large model (including interaction)
ma0 = lmer(log(amp_acc) ~ visitNum_centered*trt2 + hive +IT * treatment+ (1|beeID), data = newdf3, REML = FALSE)
summary(ma0)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## log(amp_acc) ~ visitNum_centered * trt2 + hive + IT * treatment +
## (1 | beeID)
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4541.7 4599.3 -2260.8 4521.7 2350
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0318 -0.5397 0.1116 0.6862 2.6657
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.06647 0.2578
## Residual 0.38294 0.6188
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.6249695 0.5736149 4.576
## visitNum_centered 0.0017926 0.0010587 1.693
## trt2Weighted first -0.0608425 0.0918382 -0.662
## hive4 0.0948197 0.0975308 0.972
## IT 0.0589548 0.1420758 0.415
## treatmentWeighted -1.4174293 0.3083754 -4.596
## visitNum_centered:trt2Weighted first -0.0004062 0.0020914 -0.194
## IT:treatmentWeighted 0.2808255 0.0780233 3.599
##
## Correlation of Fixed Effects:
## (Intr) vstNm_ trt2Wf hive4 IT trtmnW vN_:2f
## vstNm_cntrd -0.015
## trt2Wghtdfr -0.229 0.040
## hive4 -0.038 -0.014 -0.013
## IT -0.992 0.038 0.162 -0.014
## trtmntWghtd -0.312 0.142 0.014 -0.009 0.316
## vstNm_c:2Wf -0.022 -0.805 -0.027 0.005 -0.005 -0.002
## IT:trtmntWg 0.307 -0.241 -0.016 0.010 -0.317 -0.990 0.115ma1 = update(ma0, .~. - visitNum_centered:trt2)
BIC(ma0, ma1) # interaction, ma1, is better## df BIC
## ma0 10 4599.347
## ma1 9 4591.618# pval for interaction (in case paper needs it)
anova(ma0, ma1)## Data: newdf3
## Models:
## ma1: log(amp_acc) ~ visitNum_centered + trt2 + hive + IT + treatment +
## ma1: (1 | beeID) + IT:treatment
## ma0: log(amp_acc) ~ visitNum_centered * trt2 + hive + IT * treatment +
## ma0: (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma1 9 4539.7 4591.6 -2260.9 4521.7
## ma0 10 4541.7 4599.3 -2260.8 4521.7 0.0377 1 0.846summary(ma1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## log(amp_acc) ~ visitNum_centered + trt2 + hive + IT + treatment +
## (1 | beeID) + IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4539.7 4591.6 -2260.9 4521.7 2351
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0255 -0.5401 0.1127 0.6850 2.6689
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.06652 0.2579
## Residual 0.38294 0.6188
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.6225230 0.5736617 4.572
## visitNum_centered 0.0016270 0.0006282 2.590
## trt2Weighted first -0.0613216 0.0918373 -0.668
## hive4 0.0949225 0.0975640 0.973
## IT 0.0588142 0.1421196 0.414
## treatmentWeighted -1.4175699 0.3083761 -4.597
## IT:treatmentWeighted 0.2825651 0.0775090 3.646
##
## Correlation of Fixed Effects:
## (Intr) vstNm_ trt2Wf hive4 IT trtmnW
## vstNm_cntrd -0.055
## trt2Wghtdfr -0.229 0.031
## hive4 -0.038 -0.016 -0.013
## IT -0.993 0.056 0.162 -0.014
## trtmntWghtd -0.312 0.236 0.014 -0.009 0.316
## IT:trtmntWg 0.312 -0.253 -0.013 0.009 -0.318 -0.996ma2 <- update(ma1, .~. - trt2)
BIC(ma1, ma2) # keep ma2## df BIC
## ma1 9 4591.618
## ma2 8 4584.295summary(ma2)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: log(amp_acc) ~ visitNum_centered + hive + IT + treatment + (1 |
## beeID) + IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4538.2 4584.3 -2261.1 4522.2 2352
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0293 -0.5416 0.1160 0.6854 2.6651
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.06752 0.2598
## Residual 0.38294 0.6188
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.534726 0.561839 4.511
## visitNum_centered 0.001640 0.000628 2.611
## hive4 0.094133 0.098224 0.958
## IT 0.074144 0.141118 0.525
## treatmentWeighted -1.414972 0.308358 -4.589
## IT:treatmentWeighted 0.281940 0.077505 3.638
##
## Correlation of Fixed Effects:
## (Intr) vstNm_ hive4 IT trtmnW
## vstNm_cntrd -0.049
## hive4 -0.042 -0.016
## IT -0.995 0.052 -0.012
## trtmntWghtd -0.315 0.235 -0.008 0.316
## IT:trtmntWg 0.316 -0.252 0.009 -0.318 -0.996ma3 <- update(ma2, .~. - hive)
anova(ma2, ma3) # keep ma3## Data: newdf3
## Models:
## ma3: log(amp_acc) ~ visitNum_centered + IT + treatment + (1 | beeID) +
## ma3: IT:treatment
## ma2: log(amp_acc) ~ visitNum_centered + hive + IT + treatment + (1 |
## ma2: beeID) + IT:treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma3 7 4537.1 4577.4 -2261.5 4523.1
## ma2 8 4538.2 4584.3 -2261.1 4522.2 0.9083 1 0.3406summary(ma3)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## log(amp_acc) ~ visitNum_centered + IT + treatment + (1 | beeID) +
## IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4537.1 4577.4 -2261.5 4523.1 2353
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0319 -0.5419 0.1149 0.6887 2.6771
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.06929 0.2632
## Residual 0.38295 0.6188
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.557274 0.567438 4.507
## visitNum_centered 0.001648 0.000628 2.625
## IT 0.075722 0.142637 0.531
## treatmentWeighted -1.412882 0.308373 -4.582
## IT:treatmentWeighted 0.281383 0.077509 3.630
##
## Correlation of Fixed Effects:
## (Intr) vstNm_ IT trtmnW
## vstNm_cntrd -0.049
## IT -0.996 0.051
## trtmntWghtd -0.312 0.235 0.312
## IT:trtmntWg 0.313 -0.252 -0.315 -0.996ma3.1 <- update(ma3, .~. - visitNum_centered)
anova(ma3, ma3.1) # keep 3.1## Data: newdf3
## Models:
## ma3.1: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## ma3: log(amp_acc) ~ visitNum_centered + IT + treatment + (1 | beeID) +
## ma3: IT:treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma3.1 6 4541.9 4576.5 -2265.0 4529.9
## ma3 7 4537.1 4577.4 -2261.5 4523.1 6.877 1 0.008731 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(ma3.1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4541.9 4576.5 -2265.0 4529.9 2354
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0202 -0.5393 0.1093 0.6834 2.6666
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07006 0.2647
## Residual 0.38402 0.6197
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.63056 0.56952 4.619
## IT 0.05660 0.14315 0.395
## treatmentWeighted -1.60343 0.30014 -5.342
## IT:treatmentWeighted 0.33276 0.07511 4.431
##
## Correlation of Fixed Effects:
## (Intr) IT trtmnW
## IT -0.996
## trtmntWghtd -0.309 0.308
## IT:trtmntWg 0.310 -0.312 -0.996ma4 <- update(ma3.1, .~. - visitNum_centered )
anova(ma3.1, ma4) #keep ma3.1## Data: newdf3
## Models:
## ma3.1: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## ma4: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma3.1 6 4541.9 4576.5 -2265 4529.9
## ma4 6 4541.9 4576.5 -2265 4529.9 0 0 1summary(ma3.1)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4541.9 4576.5 -2265.0 4529.9 2354
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0202 -0.5393 0.1093 0.6834 2.6666
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07006 0.2647
## Residual 0.38402 0.6197
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.63056 0.56952 4.619
## IT 0.05660 0.14315 0.395
## treatmentWeighted -1.60343 0.30014 -5.342
## IT:treatmentWeighted 0.33276 0.07511 4.431
##
## Correlation of Fixed Effects:
## (Intr) IT trtmnW
## IT -0.996
## trtmntWghtd -0.309 0.308
## IT:trtmntWg 0.310 -0.312 -0.996m3.2 <- update(ma3.1, .~ . + I(scale(visitNum_centered)) + I(scale(visitNum_centered^2)) + (1|beeID))
summary(m3.2)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula:
## log(amp_acc) ~ IT + treatment + (1 | beeID) + I(scale(visitNum_centered)) +
## I(scale(visitNum_centered^2)) + IT:treatment
## Data: newdf3
##
## AIC BIC logLik deviance df.resid
## 4539.1 4585.2 -2261.5 4523.1 2352
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0308 -0.5413 0.1154 0.6887 2.6758
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.06929 0.2632
## Residual 0.38294 0.6188
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.56721 0.56770 4.522
## IT 0.07536 0.14273 0.528
## treatmentWeighted -1.41125 0.30921 -4.564
## I(scale(visitNum_centered)) 0.03784 0.01705 2.219
## I(scale(visitNum_centered^2)) 0.00129 0.01797 0.072
## IT:treatmentWeighted 0.28096 0.07774 3.614
##
## Correlation of Fixed Effects:
## (Intr) IT trtmnW I((N_) I((N_^
## IT -0.996
## trtmntWghtd -0.307 0.309
## I(scl(vN_)) -0.057 0.062 0.164
## I(sc(N_^2)) 0.038 -0.035 0.074 -0.511
## IT:trtmntWg 0.308 -0.311 -0.996 -0.177 -0.076anova(ma3.1, m3.2) # keep ma3.1 (according to BIC)## Data: newdf3
## Models:
## ma3.1: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## m3.2: log(amp_acc) ~ IT + treatment + (1 | beeID) + I(scale(visitNum_centered)) +
## m3.2: I(scale(visitNum_centered^2)) + IT:treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma3.1 6 4541.9 4576.5 -2265.0 4529.9
## m3.2 8 4539.1 4585.2 -2261.5 4523.1 6.8821 2 0.03203 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1finmod <- update(ma3.1, .~., REML = TRUE)
summary(finmod)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## Data: newdf3
##
## REML criterion at convergence: 4545.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0179 -0.5395 0.1071 0.6826 2.6697
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07463 0.2732
## Residual 0.38434 0.6200
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.63087 0.58488 4.498
## IT 0.05653 0.14700 0.385
## treatmentWeighted -1.60422 0.30031 -5.342
## IT:treatmentWeighted 0.33294 0.07515 4.430
##
## Correlation of Fixed Effects:
## (Intr) IT trtmnW
## IT -0.996
## trtmntWghtd -0.301 0.300
## IT:trtmntWg 0.302 -0.303 -0.996# finmod_centered <- update(ma3.1, .~. - IT*treatment + I(scale(IT, center = TRUE, scale = FALSE))*treatment, REML = TRUE)
# summary(finmod_centered)
# get p-value for interaction for paper
pvalMod <- update(ma3.1, .~. - IT:treatment)
anova(ma3.1, pvalMod)## Data: newdf3
## Models:
## pvalMod: log(amp_acc) ~ IT + treatment + (1 | beeID)
## ma3.1: log(amp_acc) ~ IT + treatment + (1 | beeID) + IT:treatment
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## pvalMod 5 4559.5 4588.3 -2274.8 4549.5
## ma3.1 6 4541.9 4576.5 -2265.0 4529.9 19.545 1 9.826e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# diagnostics
plot(finmod)
qqnorm(ranef(finmod)$beeID[[1]])
qqline(ranef(finmod)$beeID[[1]])
sjp.lmer(finmod) # plot random effects to find any outliers## Plotting random effects...
sjp.lmer(finmod, type = 'fe', sort = TRUE, p.kr = FALSE) # plot fixed effects## Computing p-values via Wald-statistics approximation (treating t as Wald z).
Bootstrap CI’s for amplitude for figure for paper
# set number of bootstrap replicates for models
nbootSims2 = 10000
# using hive 3, since it's the one with the most data
pframe <- expand.grid(trt2 = levels(droplevels(newdf3$trt2)),
IT = c(ITmean, seq(min(newdf3$IT), max(newdf3$IT), length.out = 50)),
visitNum_centered = -50:50,
hive = factor(3, levels = levels(newdf3$hive)),
beeID = 99999,
treatment = levels(droplevels(newdf3$treatment)))
pframe$amp_acc <- 0
pframe2 <- pframe[(pframe$trt2 == "Sham first" &
pframe$treatment == "Sham" &
pframe$visitNum_centered < 0) |
(pframe$trt2 == "Sham first" &
pframe$treatment == "Weighted" &
pframe$visitNum_centered > 0) |
(pframe$trt2 == "Weighted first" &
pframe$treatment == "Weighted" &
pframe$visitNum_centered < 0) |
(pframe$trt2 == "Weighted first" &
pframe$treatment == "Sham" &
pframe$visitNum_centered > 0)
, ]
# exponentiate to put on original scale
pp <- exp(predict(finmod, newdata = pframe2, re.form=NA, type = 'response')) # re.form sets all random effects to 0
### Calculate CI's (using bootstrap, not accounting for random effects)
bb2 <- bootMer(finmod, FUN=function(x) predict(x, pframe2, re.form=NA, type = 'response'), nsim = nbootSims2)## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce q
## Warning in optwrap(object@optinfo$optimizer, ff, x0, lower = lower, control
## = control$optCtrl, : convergence code 3 from bobyqa: bobyqa -- a trust
## region step failed to reduce qprint(paste("Number of bootstrap samples", nrow(bb2$t)))## [1] "Number of bootstrap samples 10000"bb2_se <-apply(bb2$t,2,function(x) quantile(x, probs = c(0.025, 0.975)))
pframe2$blo<- exp(bb2_se[1,]) # exponentiate to put on original scale
pframe2$bhi<- exp(bb2_se[2,])
pframe2$predMean <- pp
pframe2## trt2 IT visitNum_centered hive beeID treatment
## 1 Sham first 3.965833 -50 3 99999 Sham
## 3 Sham first 3.120000 -50 3 99999 Sham
## 5 Sham first 3.154490 -50 3 99999 Sham
## 7 Sham first 3.188980 -50 3 99999 Sham
## 9 Sham first 3.223469 -50 3 99999 Sham
## 11 Sham first 3.257959 -50 3 99999 Sham
## 13 Sham first 3.292449 -50 3 99999 Sham
## 15 Sham first 3.326939 -50 3 99999 Sham
## 17 Sham first 3.361429 -50 3 99999 Sham
## 19 Sham first 3.395918 -50 3 99999 Sham
## 21 Sham first 3.430408 -50 3 99999 Sham
## 23 Sham first 3.464898 -50 3 99999 Sham
## 25 Sham first 3.499388 -50 3 99999 Sham
## 27 Sham first 3.533878 -50 3 99999 Sham
## 29 Sham first 3.568367 -50 3 99999 Sham
## 31 Sham first 3.602857 -50 3 99999 Sham
## 33 Sham first 3.637347 -50 3 99999 Sham
## 35 Sham first 3.671837 -50 3 99999 Sham
## 37 Sham first 3.706327 -50 3 99999 Sham
## 39 Sham first 3.740816 -50 3 99999 Sham
## 41 Sham first 3.775306 -50 3 99999 Sham
## 43 Sham first 3.809796 -50 3 99999 Sham
## 45 Sham first 3.844286 -50 3 99999 Sham
## 47 Sham first 3.878776 -50 3 99999 Sham
## 49 Sham first 3.913265 -50 3 99999 Sham
## 51 Sham first 3.947755 -50 3 99999 Sham
## 53 Sham first 3.982245 -50 3 99999 Sham
## 55 Sham first 4.016735 -50 3 99999 Sham
## 57 Sham first 4.051224 -50 3 99999 Sham
## 59 Sham first 4.085714 -50 3 99999 Sham
## 61 Sham first 4.120204 -50 3 99999 Sham
## 63 Sham first 4.154694 -50 3 99999 Sham
## 65 Sham first 4.189184 -50 3 99999 Sham
## 67 Sham first 4.223673 -50 3 99999 Sham
## 69 Sham first 4.258163 -50 3 99999 Sham
## 71 Sham first 4.292653 -50 3 99999 Sham
## 73 Sham first 4.327143 -50 3 99999 Sham
## 75 Sham first 4.361633 -50 3 99999 Sham
## 77 Sham first 4.396122 -50 3 99999 Sham
## 79 Sham first 4.430612 -50 3 99999 Sham
## 81 Sham first 4.465102 -50 3 99999 Sham
## 83 Sham first 4.499592 -50 3 99999 Sham
## 85 Sham first 4.534082 -50 3 99999 Sham
## 87 Sham first 4.568571 -50 3 99999 Sham
## 89 Sham first 4.603061 -50 3 99999 Sham
## 91 Sham first 4.637551 -50 3 99999 Sham
## 93 Sham first 4.672041 -50 3 99999 Sham
## 95 Sham first 4.706531 -50 3 99999 Sham
## 97 Sham first 4.741020 -50 3 99999 Sham
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## 1987 Sham first 3.913265 -31 3 99999 Sham
## 1989 Sham first 3.947755 -31 3 99999 Sham
## 1991 Sham first 3.982245 -31 3 99999 Sham
## 1993 Sham first 4.016735 -31 3 99999 Sham
## 1995 Sham first 4.051224 -31 3 99999 Sham
## 1997 Sham first 4.085714 -31 3 99999 Sham
## 1999 Sham first 4.120204 -31 3 99999 Sham
## 2001 Sham first 4.154694 -31 3 99999 Sham
## 2003 Sham first 4.189184 -31 3 99999 Sham
## 2005 Sham first 4.223673 -31 3 99999 Sham
## 2007 Sham first 4.258163 -31 3 99999 Sham
## 2009 Sham first 4.292653 -31 3 99999 Sham
## 2011 Sham first 4.327143 -31 3 99999 Sham
## 2013 Sham first 4.361633 -31 3 99999 Sham
## 2015 Sham first 4.396122 -31 3 99999 Sham
## 2017 Sham first 4.430612 -31 3 99999 Sham
## 2019 Sham first 4.465102 -31 3 99999 Sham
## 2021 Sham first 4.499592 -31 3 99999 Sham
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## 20167 Sham first 4.327143 46 3 99999 Weighted
## 20169 Sham first 4.361633 46 3 99999 Weighted
## 20171 Sham first 4.396122 46 3 99999 Weighted
## 20173 Sham first 4.430612 46 3 99999 Weighted
## 20175 Sham first 4.465102 46 3 99999 Weighted
## 20177 Sham first 4.499592 46 3 99999 Weighted
## 20179 Sham first 4.534082 46 3 99999 Weighted
## 20181 Sham first 4.568571 46 3 99999 Weighted
## 20183 Sham first 4.603061 46 3 99999 Weighted
## 20185 Sham first 4.637551 46 3 99999 Weighted
## 20187 Sham first 4.672041 46 3 99999 Weighted
## 20189 Sham first 4.706531 46 3 99999 Weighted
## 20191 Sham first 4.741020 46 3 99999 Weighted
## 20193 Sham first 4.775510 46 3 99999 Weighted
## 20195 Sham first 4.810000 46 3 99999 Weighted
## 20197 Sham first 3.965833 47 3 99999 Weighted
## 20199 Sham first 3.120000 47 3 99999 Weighted
## 20201 Sham first 3.154490 47 3 99999 Weighted
## amp_acc blo bhi predMean
## 1 0 15.786755 19.11063 17.375143
## 3 0 12.747529 21.42297 16.563946
## 5 0 12.898402 21.27276 16.596271
## 7 0 13.044637 21.12472 16.628659
## 9 0 13.204147 20.96679 16.661109
## 11 0 13.360318 20.82495 16.693623
## 13 0 13.509710 20.69745 16.726201
## 15 0 13.658756 20.55649 16.758842
## 17 0 13.806695 20.41322 16.791547
## 19 0 13.953304 20.27007 16.824316
## 21 0 14.098045 20.13669 16.857148
## 23 0 14.248390 20.03043 16.890045
## 25 0 14.391244 19.92344 16.923006
## 27 0 14.534965 19.81665 16.956031
## 29 0 14.674231 19.71432 16.989120
## 31 0 14.801743 19.59719 17.022275
## 33 0 14.939533 19.48632 17.055494
## 35 0 15.068288 19.38951 17.088777
## 37 0 15.188868 19.29975 17.122126
## 39 0 15.301153 19.23375 17.155540
## 41 0 15.415208 19.14678 17.189019
## 43 0 15.510783 19.11594 17.222563
## 45 0 15.594977 19.07619 17.256173
## 47 0 15.666168 19.07005 17.289848
## 49 0 15.727019 19.06893 17.323589
## 51 0 15.774818 19.08666 17.357396
## 53 0 15.800921 19.13637 17.391269
## 55 0 15.808482 19.19543 17.425208
## 57 0 15.813018 19.26397 17.459213
## 59 0 15.784327 19.36724 17.493285
## 61 0 15.759337 19.48890 17.527423
## 63 0 15.722763 19.60425 17.561628
## 65 0 15.665611 19.75859 17.595899
## 67 0 15.599953 19.91694 17.630238
## 69 0 15.517456 20.08118 17.664643
## 71 0 15.446045 20.23426 17.699115
## 73 0 15.356553 20.41402 17.733655
## 75 0 15.273920 20.61788 17.768262
## 77 0 15.179424 20.80965 17.802937
## 79 0 15.076522 21.02060 17.837679
## 81 0 14.979612 21.25003 17.872490
## 83 0 14.871893 21.47613 17.907368
## 85 0 14.770738 21.72285 17.942314
## 87 0 14.670429 21.93441 17.977328
## 89 0 14.559271 22.17627 18.012411
## 91 0 14.456782 22.41026 18.047562
## 93 0 14.354868 22.69217 18.082782
## 95 0 14.262584 22.94351 18.118070
## 97 0 14.167677 23.19956 18.153428
## 99 0 14.075860 23.46347 18.188854
## 101 0 13.981751 23.71705 18.224349
## 103 0 15.786755 19.11063 17.375143
## 105 0 12.747529 21.42297 16.563946
## 107 0 12.898402 21.27276 16.596271
## 109 0 13.044637 21.12472 16.628659
## 111 0 13.204147 20.96679 16.661109
## 113 0 13.360318 20.82495 16.693623
## 115 0 13.509710 20.69745 16.726201
## 117 0 13.658756 20.55649 16.758842
## 119 0 13.806695 20.41322 16.791547
## 121 0 13.953304 20.27007 16.824316
## 123 0 14.098045 20.13669 16.857148
## 125 0 14.248390 20.03043 16.890045
## 127 0 14.391244 19.92344 16.923006
## 129 0 14.534965 19.81665 16.956031
## 131 0 14.674231 19.71432 16.989120
## 133 0 14.801743 19.59719 17.022275
## 135 0 14.939533 19.48632 17.055494
## 137 0 15.068288 19.38951 17.088777
## 139 0 15.188868 19.29975 17.122126
## 141 0 15.301153 19.23375 17.155540
## 143 0 15.415208 19.14678 17.189019
## 145 0 15.510783 19.11594 17.222563
## 147 0 15.594977 19.07619 17.256173
## 149 0 15.666168 19.07005 17.289848
## 151 0 15.727019 19.06893 17.323589
## 153 0 15.774818 19.08666 17.357396
## 155 0 15.800921 19.13637 17.391269
## 157 0 15.808482 19.19543 17.425208
## 159 0 15.813018 19.26397 17.459213
## 161 0 15.784327 19.36724 17.493285
## 163 0 15.759337 19.48890 17.527423
## 165 0 15.722763 19.60425 17.561628
## 167 0 15.665611 19.75859 17.595899
## 169 0 15.599953 19.91694 17.630238
## 171 0 15.517456 20.08118 17.664643
## 173 0 15.446045 20.23426 17.699115
## 175 0 15.356553 20.41402 17.733655
## 177 0 15.273920 20.61788 17.768262
## 179 0 15.179424 20.80965 17.802937
## 181 0 15.076522 21.02060 17.837679
## 183 0 14.979612 21.25003 17.872490
## 185 0 14.871893 21.47613 17.907368
## 187 0 14.770738 21.72285 17.942314
## 189 0 14.670429 21.93441 17.977328
## 191 0 14.559271 22.17627 18.012411
## 193 0 14.456782 22.41026 18.047562
## 195 0 14.354868 22.69217 18.082782
## 197 0 14.262584 22.94351 18.118070
## 199 0 14.167677 23.19956 18.153428
## 201 0 14.075860 23.46347 18.188854
## 203 0 13.981751 23.71705 18.224349
## 205 0 15.786755 19.11063 17.375143
## 207 0 12.747529 21.42297 16.563946
## 209 0 12.898402 21.27276 16.596271
## 211 0 13.044637 21.12472 16.628659
## 213 0 13.204147 20.96679 16.661109
## 215 0 13.360318 20.82495 16.693623
## 217 0 13.509710 20.69745 16.726201
## 219 0 13.658756 20.55649 16.758842
## 221 0 13.806695 20.41322 16.791547
## 223 0 13.953304 20.27007 16.824316
## 225 0 14.098045 20.13669 16.857148
## 227 0 14.248390 20.03043 16.890045
## 229 0 14.391244 19.92344 16.923006
## 231 0 14.534965 19.81665 16.956031
## 233 0 14.674231 19.71432 16.989120
## 235 0 14.801743 19.59719 17.022275
## 237 0 14.939533 19.48632 17.055494
## 239 0 15.068288 19.38951 17.088777
## 241 0 15.188868 19.29975 17.122126
## 243 0 15.301153 19.23375 17.155540
## 245 0 15.415208 19.14678 17.189019
## 247 0 15.510783 19.11594 17.222563
## 249 0 15.594977 19.07619 17.256173
## 251 0 15.666168 19.07005 17.289848
## 253 0 15.727019 19.06893 17.323589
## 255 0 15.774818 19.08666 17.357396
## 257 0 15.800921 19.13637 17.391269
## 259 0 15.808482 19.19543 17.425208
## 261 0 15.813018 19.26397 17.459213
## 263 0 15.784327 19.36724 17.493285
## 265 0 15.759337 19.48890 17.527423
## 267 0 15.722763 19.60425 17.561628
## 269 0 15.665611 19.75859 17.595899
## 271 0 15.599953 19.91694 17.630238
## 273 0 15.517456 20.08118 17.664643
## 275 0 15.446045 20.23426 17.699115
## 277 0 15.356553 20.41402 17.733655
## 279 0 15.273920 20.61788 17.768262
## 281 0 15.179424 20.80965 17.802937
## 283 0 15.076522 21.02060 17.837679
## 285 0 14.979612 21.25003 17.872490
## 287 0 14.871893 21.47613 17.907368
## 289 0 14.770738 21.72285 17.942314
## 291 0 14.670429 21.93441 17.977328
## 293 0 14.559271 22.17627 18.012411
## 295 0 14.456782 22.41026 18.047562
## 297 0 14.354868 22.69217 18.082782
## 299 0 14.262584 22.94351 18.118070
## 301 0 14.167677 23.19956 18.153428
## 303 0 14.075860 23.46347 18.188854
## 305 0 13.981751 23.71705 18.224349
## 307 0 15.786755 19.11063 17.375143
## 309 0 12.747529 21.42297 16.563946
## 311 0 12.898402 21.27276 16.596271
## 313 0 13.044637 21.12472 16.628659
## 315 0 13.204147 20.96679 16.661109
## 317 0 13.360318 20.82495 16.693623
## 319 0 13.509710 20.69745 16.726201
## 321 0 13.658756 20.55649 16.758842
## 323 0 13.806695 20.41322 16.791547
## 325 0 13.953304 20.27007 16.824316
## 327 0 14.098045 20.13669 16.857148
## 329 0 14.248390 20.03043 16.890045
## 331 0 14.391244 19.92344 16.923006
## 333 0 14.534965 19.81665 16.956031
## 335 0 14.674231 19.71432 16.989120
## 337 0 14.801743 19.59719 17.022275
## 339 0 14.939533 19.48632 17.055494
## 341 0 15.068288 19.38951 17.088777
## 343 0 15.188868 19.29975 17.122126
## 345 0 15.301153 19.23375 17.155540
## 347 0 15.415208 19.14678 17.189019
## 349 0 15.510783 19.11594 17.222563
## 351 0 15.594977 19.07619 17.256173
## 353 0 15.666168 19.07005 17.289848
## 355 0 15.727019 19.06893 17.323589
## 357 0 15.774818 19.08666 17.357396
## 359 0 15.800921 19.13637 17.391269
## 361 0 15.808482 19.19543 17.425208
## 363 0 15.813018 19.26397 17.459213
## 365 0 15.784327 19.36724 17.493285
## 367 0 15.759337 19.48890 17.527423
## 369 0 15.722763 19.60425 17.561628
## 371 0 15.665611 19.75859 17.595899
## 373 0 15.599953 19.91694 17.630238
## 375 0 15.517456 20.08118 17.664643
## 377 0 15.446045 20.23426 17.699115
## 379 0 15.356553 20.41402 17.733655
## 381 0 15.273920 20.61788 17.768262
## 383 0 15.179424 20.80965 17.802937
## 385 0 15.076522 21.02060 17.837679
## 387 0 14.979612 21.25003 17.872490
## 389 0 14.871893 21.47613 17.907368
## 391 0 14.770738 21.72285 17.942314
## 393 0 14.670429 21.93441 17.977328
## 395 0 14.559271 22.17627 18.012411
## 397 0 14.456782 22.41026 18.047562
## 399 0 14.354868 22.69217 18.082782
## 401 0 14.262584 22.94351 18.118070
## 403 0 14.167677 23.19956 18.153428
## 405 0 14.075860 23.46347 18.188854
## 407 0 13.981751 23.71705 18.224349
## 409 0 15.786755 19.11063 17.375143
## 411 0 12.747529 21.42297 16.563946
## 413 0 12.898402 21.27276 16.596271
## 415 0 13.044637 21.12472 16.628659
## 417 0 13.204147 20.96679 16.661109
## 419 0 13.360318 20.82495 16.693623
## 421 0 13.509710 20.69745 16.726201
## 423 0 13.658756 20.55649 16.758842
## 425 0 13.806695 20.41322 16.791547
## 427 0 13.953304 20.27007 16.824316
## 429 0 14.098045 20.13669 16.857148
## 431 0 14.248390 20.03043 16.890045
## 433 0 14.391244 19.92344 16.923006
## 435 0 14.534965 19.81665 16.956031
## 437 0 14.674231 19.71432 16.989120
## 439 0 14.801743 19.59719 17.022275
## 441 0 14.939533 19.48632 17.055494
## 443 0 15.068288 19.38951 17.088777
## 445 0 15.188868 19.29975 17.122126
## 447 0 15.301153 19.23375 17.155540
## 449 0 15.415208 19.14678 17.189019
## 451 0 15.510783 19.11594 17.222563
## 453 0 15.594977 19.07619 17.256173
## 455 0 15.666168 19.07005 17.289848
## 457 0 15.727019 19.06893 17.323589
## 459 0 15.774818 19.08666 17.357396
## 461 0 15.800921 19.13637 17.391269
## 463 0 15.808482 19.19543 17.425208
## 465 0 15.813018 19.26397 17.459213
## 467 0 15.784327 19.36724 17.493285
## 469 0 15.759337 19.48890 17.527423
## 471 0 15.722763 19.60425 17.561628
## 473 0 15.665611 19.75859 17.595899
## 475 0 15.599953 19.91694 17.630238
## 477 0 15.517456 20.08118 17.664643
## 479 0 15.446045 20.23426 17.699115
## 481 0 15.356553 20.41402 17.733655
## 483 0 15.273920 20.61788 17.768262
## 485 0 15.179424 20.80965 17.802937
## 487 0 15.076522 21.02060 17.837679
## 489 0 14.979612 21.25003 17.872490
## 491 0 14.871893 21.47613 17.907368
## 493 0 14.770738 21.72285 17.942314
## 495 0 14.670429 21.93441 17.977328
## 497 0 14.559271 22.17627 18.012411
## 499 0 14.456782 22.41026 18.047562
## 501 0 14.354868 22.69217 18.082782
## 503 0 14.262584 22.94351 18.118070
## 505 0 14.167677 23.19956 18.153428
## 507 0 14.075860 23.46347 18.188854
## 509 0 13.981751 23.71705 18.224349
## 511 0 15.786755 19.11063 17.375143
## 513 0 12.747529 21.42297 16.563946
## 515 0 12.898402 21.27276 16.596271
## 517 0 13.044637 21.12472 16.628659
## 519 0 13.204147 20.96679 16.661109
## 521 0 13.360318 20.82495 16.693623
## 523 0 13.509710 20.69745 16.726201
## 525 0 13.658756 20.55649 16.758842
## 527 0 13.806695 20.41322 16.791547
## 529 0 13.953304 20.27007 16.824316
## 531 0 14.098045 20.13669 16.857148
## 533 0 14.248390 20.03043 16.890045
## 535 0 14.391244 19.92344 16.923006
## 537 0 14.534965 19.81665 16.956031
## 539 0 14.674231 19.71432 16.989120
## 541 0 14.801743 19.59719 17.022275
## 543 0 14.939533 19.48632 17.055494
## 545 0 15.068288 19.38951 17.088777
## 547 0 15.188868 19.29975 17.122126
## 549 0 15.301153 19.23375 17.155540
## 551 0 15.415208 19.14678 17.189019
## 553 0 15.510783 19.11594 17.222563
## 555 0 15.594977 19.07619 17.256173
## 557 0 15.666168 19.07005 17.289848
## 559 0 15.727019 19.06893 17.323589
## 561 0 15.774818 19.08666 17.357396
## 563 0 15.800921 19.13637 17.391269
## 565 0 15.808482 19.19543 17.425208
## 567 0 15.813018 19.26397 17.459213
## 569 0 15.784327 19.36724 17.493285
## 571 0 15.759337 19.48890 17.527423
## 573 0 15.722763 19.60425 17.561628
## 575 0 15.665611 19.75859 17.595899
## 577 0 15.599953 19.91694 17.630238
## 579 0 15.517456 20.08118 17.664643
## 581 0 15.446045 20.23426 17.699115
## 583 0 15.356553 20.41402 17.733655
## 585 0 15.273920 20.61788 17.768262
## 587 0 15.179424 20.80965 17.802937
## 589 0 15.076522 21.02060 17.837679
## 591 0 14.979612 21.25003 17.872490
## 593 0 14.871893 21.47613 17.907368
## 595 0 14.770738 21.72285 17.942314
## 597 0 14.670429 21.93441 17.977328
## 599 0 14.559271 22.17627 18.012411
## 601 0 14.456782 22.41026 18.047562
## 603 0 14.354868 22.69217 18.082782
## 605 0 14.262584 22.94351 18.118070
## 607 0 14.167677 23.19956 18.153428
## 609 0 14.075860 23.46347 18.188854
## 611 0 13.981751 23.71705 18.224349
## 613 0 15.786755 19.11063 17.375143
## 615 0 12.747529 21.42297 16.563946
## 617 0 12.898402 21.27276 16.596271
## 619 0 13.044637 21.12472 16.628659
## 621 0 13.204147 20.96679 16.661109
## 623 0 13.360318 20.82495 16.693623
## 625 0 13.509710 20.69745 16.726201
## 627 0 13.658756 20.55649 16.758842
## 629 0 13.806695 20.41322 16.791547
## 631 0 13.953304 20.27007 16.824316
## 633 0 14.098045 20.13669 16.857148
## 635 0 14.248390 20.03043 16.890045
## 637 0 14.391244 19.92344 16.923006
## 639 0 14.534965 19.81665 16.956031
## 641 0 14.674231 19.71432 16.989120
## 643 0 14.801743 19.59719 17.022275
## 645 0 14.939533 19.48632 17.055494
## 647 0 15.068288 19.38951 17.088777
## 649 0 15.188868 19.29975 17.122126
## 651 0 15.301153 19.23375 17.155540
## 653 0 15.415208 19.14678 17.189019
## 655 0 15.510783 19.11594 17.222563
## 657 0 15.594977 19.07619 17.256173
## 659 0 15.666168 19.07005 17.289848
## 661 0 15.727019 19.06893 17.323589
## 663 0 15.774818 19.08666 17.357396
## 665 0 15.800921 19.13637 17.391269
## 667 0 15.808482 19.19543 17.425208
## 669 0 15.813018 19.26397 17.459213
## 671 0 15.784327 19.36724 17.493285
## 673 0 15.759337 19.48890 17.527423
## 675 0 15.722763 19.60425 17.561628
## 677 0 15.665611 19.75859 17.595899
## 679 0 15.599953 19.91694 17.630238
## 681 0 15.517456 20.08118 17.664643
## 683 0 15.446045 20.23426 17.699115
## 685 0 15.356553 20.41402 17.733655
## 687 0 15.273920 20.61788 17.768262
## 689 0 15.179424 20.80965 17.802937
## 691 0 15.076522 21.02060 17.837679
## 693 0 14.979612 21.25003 17.872490
## 695 0 14.871893 21.47613 17.907368
## 697 0 14.770738 21.72285 17.942314
## 699 0 14.670429 21.93441 17.977328
## 701 0 14.559271 22.17627 18.012411
## 703 0 14.456782 22.41026 18.047562
## 705 0 14.354868 22.69217 18.082782
## 707 0 14.262584 22.94351 18.118070
## 709 0 14.167677 23.19956 18.153428
## 711 0 14.075860 23.46347 18.188854
## 713 0 13.981751 23.71705 18.224349
## 715 0 15.786755 19.11063 17.375143
## 717 0 12.747529 21.42297 16.563946
## 719 0 12.898402 21.27276 16.596271
## 721 0 13.044637 21.12472 16.628659
## 723 0 13.204147 20.96679 16.661109
## 725 0 13.360318 20.82495 16.693623
## 727 0 13.509710 20.69745 16.726201
## 729 0 13.658756 20.55649 16.758842
## 731 0 13.806695 20.41322 16.791547
## 733 0 13.953304 20.27007 16.824316
## 735 0 14.098045 20.13669 16.857148
## 737 0 14.248390 20.03043 16.890045
## 739 0 14.391244 19.92344 16.923006
## 741 0 14.534965 19.81665 16.956031
## 743 0 14.674231 19.71432 16.989120
## 745 0 14.801743 19.59719 17.022275
## 747 0 14.939533 19.48632 17.055494
## 749 0 15.068288 19.38951 17.088777
## 751 0 15.188868 19.29975 17.122126
## 753 0 15.301153 19.23375 17.155540
## 755 0 15.415208 19.14678 17.189019
## 757 0 15.510783 19.11594 17.222563
## 759 0 15.594977 19.07619 17.256173
## 761 0 15.666168 19.07005 17.289848
## 763 0 15.727019 19.06893 17.323589
## 765 0 15.774818 19.08666 17.357396
## 767 0 15.800921 19.13637 17.391269
## 769 0 15.808482 19.19543 17.425208
## 771 0 15.813018 19.26397 17.459213
## 773 0 15.784327 19.36724 17.493285
## 775 0 15.759337 19.48890 17.527423
## 777 0 15.722763 19.60425 17.561628
## 779 0 15.665611 19.75859 17.595899
## 781 0 15.599953 19.91694 17.630238
## 783 0 15.517456 20.08118 17.664643
## 785 0 15.446045 20.23426 17.699115
## 787 0 15.356553 20.41402 17.733655
## 789 0 15.273920 20.61788 17.768262
## 791 0 15.179424 20.80965 17.802937
## 793 0 15.076522 21.02060 17.837679
## 795 0 14.979612 21.25003 17.872490
## 797 0 14.871893 21.47613 17.907368
## 799 0 14.770738 21.72285 17.942314
## 801 0 14.670429 21.93441 17.977328
## 803 0 14.559271 22.17627 18.012411
## 805 0 14.456782 22.41026 18.047562
## 807 0 14.354868 22.69217 18.082782
## 809 0 14.262584 22.94351 18.118070
## 811 0 14.167677 23.19956 18.153428
## 813 0 14.075860 23.46347 18.188854
## 815 0 13.981751 23.71705 18.224349
## 817 0 15.786755 19.11063 17.375143
## 819 0 12.747529 21.42297 16.563946
## 821 0 12.898402 21.27276 16.596271
## 823 0 13.044637 21.12472 16.628659
## 825 0 13.204147 20.96679 16.661109
## 827 0 13.360318 20.82495 16.693623
## 829 0 13.509710 20.69745 16.726201
## 831 0 13.658756 20.55649 16.758842
## 833 0 13.806695 20.41322 16.791547
## 835 0 13.953304 20.27007 16.824316
## 837 0 14.098045 20.13669 16.857148
## 839 0 14.248390 20.03043 16.890045
## 841 0 14.391244 19.92344 16.923006
## 843 0 14.534965 19.81665 16.956031
## 845 0 14.674231 19.71432 16.989120
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## 1691 0 15.784327 19.36724 17.493285
## 1693 0 15.759337 19.48890 17.527423
## 1695 0 15.722763 19.60425 17.561628
## 1697 0 15.665611 19.75859 17.595899
## 1699 0 15.599953 19.91694 17.630238
## 1701 0 15.517456 20.08118 17.664643
## 1703 0 15.446045 20.23426 17.699115
## 1705 0 15.356553 20.41402 17.733655
## 1707 0 15.273920 20.61788 17.768262
## 1709 0 15.179424 20.80965 17.802937
## 1711 0 15.076522 21.02060 17.837679
## 1713 0 14.979612 21.25003 17.872490
## 1715 0 14.871893 21.47613 17.907368
## 1717 0 14.770738 21.72285 17.942314
## 1719 0 14.670429 21.93441 17.977328
## 1721 0 14.559271 22.17627 18.012411
## 1723 0 14.456782 22.41026 18.047562
## 1725 0 14.354868 22.69217 18.082782
## 1727 0 14.262584 22.94351 18.118070
## 1729 0 14.167677 23.19956 18.153428
## 1731 0 14.075860 23.46347 18.188854
## 1733 0 13.981751 23.71705 18.224349
## 1735 0 15.786755 19.11063 17.375143
## 1737 0 12.747529 21.42297 16.563946
## 1739 0 12.898402 21.27276 16.596271
## 1741 0 13.044637 21.12472 16.628659
## 1743 0 13.204147 20.96679 16.661109
## 1745 0 13.360318 20.82495 16.693623
## 1747 0 13.509710 20.69745 16.726201
## 1749 0 13.658756 20.55649 16.758842
## 1751 0 13.806695 20.41322 16.791547
## 1753 0 13.953304 20.27007 16.824316
## 1755 0 14.098045 20.13669 16.857148
## 1757 0 14.248390 20.03043 16.890045
## 1759 0 14.391244 19.92344 16.923006
## 1761 0 14.534965 19.81665 16.956031
## 1763 0 14.674231 19.71432 16.989120
## 1765 0 14.801743 19.59719 17.022275
## 1767 0 14.939533 19.48632 17.055494
## 1769 0 15.068288 19.38951 17.088777
## 1771 0 15.188868 19.29975 17.122126
## 1773 0 15.301153 19.23375 17.155540
## 1775 0 15.415208 19.14678 17.189019
## 1777 0 15.510783 19.11594 17.222563
## 1779 0 15.594977 19.07619 17.256173
## 1781 0 15.666168 19.07005 17.289848
## 1783 0 15.727019 19.06893 17.323589
## 1785 0 15.774818 19.08666 17.357396
## 1787 0 15.800921 19.13637 17.391269
## 1789 0 15.808482 19.19543 17.425208
## 1791 0 15.813018 19.26397 17.459213
## 1793 0 15.784327 19.36724 17.493285
## 1795 0 15.759337 19.48890 17.527423
## 1797 0 15.722763 19.60425 17.561628
## 1799 0 15.665611 19.75859 17.595899
## 1801 0 15.599953 19.91694 17.630238
## 1803 0 15.517456 20.08118 17.664643
## 1805 0 15.446045 20.23426 17.699115
## 1807 0 15.356553 20.41402 17.733655
## 1809 0 15.273920 20.61788 17.768262
## 1811 0 15.179424 20.80965 17.802937
## 1813 0 15.076522 21.02060 17.837679
## 1815 0 14.979612 21.25003 17.872490
## 1817 0 14.871893 21.47613 17.907368
## 1819 0 14.770738 21.72285 17.942314
## 1821 0 14.670429 21.93441 17.977328
## 1823 0 14.559271 22.17627 18.012411
## 1825 0 14.456782 22.41026 18.047562
## 1827 0 14.354868 22.69217 18.082782
## 1829 0 14.262584 22.94351 18.118070
## 1831 0 14.167677 23.19956 18.153428
## 1833 0 14.075860 23.46347 18.188854
## 1835 0 13.981751 23.71705 18.224349
## 1837 0 15.786755 19.11063 17.375143
## 1839 0 12.747529 21.42297 16.563946
## 1841 0 12.898402 21.27276 16.596271
## 1843 0 13.044637 21.12472 16.628659
## 1845 0 13.204147 20.96679 16.661109
## 1847 0 13.360318 20.82495 16.693623
## 1849 0 13.509710 20.69745 16.726201
## 1851 0 13.658756 20.55649 16.758842
## 1853 0 13.806695 20.41322 16.791547
## 1855 0 13.953304 20.27007 16.824316
## 1857 0 14.098045 20.13669 16.857148
## 1859 0 14.248390 20.03043 16.890045
## 1861 0 14.391244 19.92344 16.923006
## 1863 0 14.534965 19.81665 16.956031
## 1865 0 14.674231 19.71432 16.989120
## 1867 0 14.801743 19.59719 17.022275
## 1869 0 14.939533 19.48632 17.055494
## 1871 0 15.068288 19.38951 17.088777
## 1873 0 15.188868 19.29975 17.122126
## 1875 0 15.301153 19.23375 17.155540
## 1877 0 15.415208 19.14678 17.189019
## 1879 0 15.510783 19.11594 17.222563
## 1881 0 15.594977 19.07619 17.256173
## 1883 0 15.666168 19.07005 17.289848
## 1885 0 15.727019 19.06893 17.323589
## 1887 0 15.774818 19.08666 17.357396
## 1889 0 15.800921 19.13637 17.391269
## 1891 0 15.808482 19.19543 17.425208
## 1893 0 15.813018 19.26397 17.459213
## 1895 0 15.784327 19.36724 17.493285
## 1897 0 15.759337 19.48890 17.527423
## 1899 0 15.722763 19.60425 17.561628
## 1901 0 15.665611 19.75859 17.595899
## 1903 0 15.599953 19.91694 17.630238
## 1905 0 15.517456 20.08118 17.664643
## 1907 0 15.446045 20.23426 17.699115
## 1909 0 15.356553 20.41402 17.733655
## 1911 0 15.273920 20.61788 17.768262
## 1913 0 15.179424 20.80965 17.802937
## 1915 0 15.076522 21.02060 17.837679
## 1917 0 14.979612 21.25003 17.872490
## 1919 0 14.871893 21.47613 17.907368
## 1921 0 14.770738 21.72285 17.942314
## 1923 0 14.670429 21.93441 17.977328
## 1925 0 14.559271 22.17627 18.012411
## 1927 0 14.456782 22.41026 18.047562
## 1929 0 14.354868 22.69217 18.082782
## 1931 0 14.262584 22.94351 18.118070
## 1933 0 14.167677 23.19956 18.153428
## 1935 0 14.075860 23.46347 18.188854
## 1937 0 13.981751 23.71705 18.224349
## 1939 0 15.786755 19.11063 17.375143
## 1941 0 12.747529 21.42297 16.563946
## 1943 0 12.898402 21.27276 16.596271
## 1945 0 13.044637 21.12472 16.628659
## 1947 0 13.204147 20.96679 16.661109
## 1949 0 13.360318 20.82495 16.693623
## 1951 0 13.509710 20.69745 16.726201
## 1953 0 13.658756 20.55649 16.758842
## 1955 0 13.806695 20.41322 16.791547
## 1957 0 13.953304 20.27007 16.824316
## 1959 0 14.098045 20.13669 16.857148
## 1961 0 14.248390 20.03043 16.890045
## 1963 0 14.391244 19.92344 16.923006
## 1965 0 14.534965 19.81665 16.956031
## 1967 0 14.674231 19.71432 16.989120
## 1969 0 14.801743 19.59719 17.022275
## 1971 0 14.939533 19.48632 17.055494
## 1973 0 15.068288 19.38951 17.088777
## 1975 0 15.188868 19.29975 17.122126
## 1977 0 15.301153 19.23375 17.155540
## 1979 0 15.415208 19.14678 17.189019
## 1981 0 15.510783 19.11594 17.222563
## 1983 0 15.594977 19.07619 17.256173
## 1985 0 15.666168 19.07005 17.289848
## 1987 0 15.727019 19.06893 17.323589
## 1989 0 15.774818 19.08666 17.357396
## 1991 0 15.800921 19.13637 17.391269
## 1993 0 15.808482 19.19543 17.425208
## 1995 0 15.813018 19.26397 17.459213
## 1997 0 15.784327 19.36724 17.493285
## 1999 0 15.759337 19.48890 17.527423
## 2001 0 15.722763 19.60425 17.561628
## 2003 0 15.665611 19.75859 17.595899
## 2005 0 15.599953 19.91694 17.630238
## 2007 0 15.517456 20.08118 17.664643
## 2009 0 15.446045 20.23426 17.699115
## 2011 0 15.356553 20.41402 17.733655
## 2013 0 15.273920 20.61788 17.768262
## 2015 0 15.179424 20.80965 17.802937
## 2017 0 15.076522 21.02060 17.837679
## 2019 0 14.979612 21.25003 17.872490
## 2021 0 14.871893 21.47613 17.907368
## 2023 0 14.770738 21.72285 17.942314
## 2025 0 14.670429 21.93441 17.977328
## 2027 0 14.559271 22.17627 18.012411
## 2029 0 14.456782 22.41026 18.047562
## 2031 0 14.354868 22.69217 18.082782
## 2033 0 14.262584 22.94351 18.118070
## 2035 0 14.167677 23.19956 18.153428
## 2037 0 14.075860 23.46347 18.188854
## 2039 0 13.981751 23.71705 18.224349
## 2041 0 15.786755 19.11063 17.375143
## 2043 0 12.747529 21.42297 16.563946
## 2045 0 12.898402 21.27276 16.596271
## 2047 0 13.044637 21.12472 16.628659
## 2049 0 13.204147 20.96679 16.661109
## 2051 0 13.360318 20.82495 16.693623
## 2053 0 13.509710 20.69745 16.726201
## 2055 0 13.658756 20.55649 16.758842
## 2057 0 13.806695 20.41322 16.791547
## 2059 0 13.953304 20.27007 16.824316
## 2061 0 14.098045 20.13669 16.857148
## 2063 0 14.248390 20.03043 16.890045
## 2065 0 14.391244 19.92344 16.923006
## 2067 0 14.534965 19.81665 16.956031
## 2069 0 14.674231 19.71432 16.989120
## 2071 0 14.801743 19.59719 17.022275
## 2073 0 14.939533 19.48632 17.055494
## 2075 0 15.068288 19.38951 17.088777
## 2077 0 15.188868 19.29975 17.122126
## 2079 0 15.301153 19.23375 17.155540
## 2081 0 15.415208 19.14678 17.189019
## 2083 0 15.510783 19.11594 17.222563
## 2085 0 15.594977 19.07619 17.256173
## 2087 0 15.666168 19.07005 17.289848
## 2089 0 15.727019 19.06893 17.323589
## 2091 0 15.774818 19.08666 17.357396
## 2093 0 15.800921 19.13637 17.391269
## 2095 0 15.808482 19.19543 17.425208
## 2097 0 15.813018 19.26397 17.459213
## 2099 0 15.784327 19.36724 17.493285
## 2101 0 15.759337 19.48890 17.527423
## 2103 0 15.722763 19.60425 17.561628
## 2105 0 15.665611 19.75859 17.595899
## 2107 0 15.599953 19.91694 17.630238
## 2109 0 15.517456 20.08118 17.664643
## 2111 0 15.446045 20.23426 17.699115
## 2113 0 15.356553 20.41402 17.733655
## 2115 0 15.273920 20.61788 17.768262
## 2117 0 15.179424 20.80965 17.802937
## 2119 0 15.076522 21.02060 17.837679
## 2121 0 14.979612 21.25003 17.872490
## 2123 0 14.871893 21.47613 17.907368
## 2125 0 14.770738 21.72285 17.942314
## 2127 0 14.670429 21.93441 17.977328
## 2129 0 14.559271 22.17627 18.012411
## 2131 0 14.456782 22.41026 18.047562
## 2133 0 14.354868 22.69217 18.082782
## 2135 0 14.262584 22.94351 18.118070
## 2137 0 14.167677 23.19956 18.153428
## 2139 0 14.075860 23.46347 18.188854
## 2141 0 13.981751 23.71705 18.224349
## 2143 0 15.786755 19.11063 17.375143
## 2145 0 12.747529 21.42297 16.563946
## 2147 0 12.898402 21.27276 16.596271
## 2149 0 13.044637 21.12472 16.628659
## 2151 0 13.204147 20.96679 16.661109
## 2153 0 13.360318 20.82495 16.693623
## 2155 0 13.509710 20.69745 16.726201
## 2157 0 13.658756 20.55649 16.758842
## 2159 0 13.806695 20.41322 16.791547
## 2161 0 13.953304 20.27007 16.824316
## 2163 0 14.098045 20.13669 16.857148
## 2165 0 14.248390 20.03043 16.890045
## 2167 0 14.391244 19.92344 16.923006
## 2169 0 14.534965 19.81665 16.956031
## 2171 0 14.674231 19.71432 16.989120
## 2173 0 14.801743 19.59719 17.022275
## 2175 0 14.939533 19.48632 17.055494
## 2177 0 15.068288 19.38951 17.088777
## 2179 0 15.188868 19.29975 17.122126
## 2181 0 15.301153 19.23375 17.155540
## 2183 0 15.415208 19.14678 17.189019
## 2185 0 15.510783 19.11594 17.222563
## 2187 0 15.594977 19.07619 17.256173
## 2189 0 15.666168 19.07005 17.289848
## 2191 0 15.727019 19.06893 17.323589
## 2193 0 15.774818 19.08666 17.357396
## 2195 0 15.800921 19.13637 17.391269
## 2197 0 15.808482 19.19543 17.425208
## 2199 0 15.813018 19.26397 17.459213
## 2201 0 15.784327 19.36724 17.493285
## 2203 0 15.759337 19.48890 17.527423
## 2205 0 15.722763 19.60425 17.561628
## 2207 0 15.665611 19.75859 17.595899
## 2209 0 15.599953 19.91694 17.630238
## 2211 0 15.517456 20.08118 17.664643
## 2213 0 15.446045 20.23426 17.699115
## 2215 0 15.356553 20.41402 17.733655
## 2217 0 15.273920 20.61788 17.768262
## 2219 0 15.179424 20.80965 17.802937
## 2221 0 15.076522 21.02060 17.837679
## 2223 0 14.979612 21.25003 17.872490
## 2225 0 14.871893 21.47613 17.907368
## 2227 0 14.770738 21.72285 17.942314
## 2229 0 14.670429 21.93441 17.977328
## 2231 0 14.559271 22.17627 18.012411
## 2233 0 14.456782 22.41026 18.047562
## 2235 0 14.354868 22.69217 18.082782
## 2237 0 14.262584 22.94351 18.118070
## 2239 0 14.167677 23.19956 18.153428
## 2241 0 14.075860 23.46347 18.188854
## 2243 0 13.981751 23.71705 18.224349
## 2245 0 15.786755 19.11063 17.375143
## 2247 0 12.747529 21.42297 16.563946
## 2249 0 12.898402 21.27276 16.596271
## 2251 0 13.044637 21.12472 16.628659
## 2253 0 13.204147 20.96679 16.661109
## 2255 0 13.360318 20.82495 16.693623
## 2257 0 13.509710 20.69745 16.726201
## 2259 0 13.658756 20.55649 16.758842
## 2261 0 13.806695 20.41322 16.791547
## 2263 0 13.953304 20.27007 16.824316
## 2265 0 14.098045 20.13669 16.857148
## 2267 0 14.248390 20.03043 16.890045
## 2269 0 14.391244 19.92344 16.923006
## 2271 0 14.534965 19.81665 16.956031
## 2273 0 14.674231 19.71432 16.989120
## 2275 0 14.801743 19.59719 17.022275
## 2277 0 14.939533 19.48632 17.055494
## 2279 0 15.068288 19.38951 17.088777
## 2281 0 15.188868 19.29975 17.122126
## 2283 0 15.301153 19.23375 17.155540
## 2285 0 15.415208 19.14678 17.189019
## 2287 0 15.510783 19.11594 17.222563
## 2289 0 15.594977 19.07619 17.256173
## 2291 0 15.666168 19.07005 17.289848
## 2293 0 15.727019 19.06893 17.323589
## 2295 0 15.774818 19.08666 17.357396
## 2297 0 15.800921 19.13637 17.391269
## 2299 0 15.808482 19.19543 17.425208
## 2301 0 15.813018 19.26397 17.459213
## 2303 0 15.784327 19.36724 17.493285
## 2305 0 15.759337 19.48890 17.527423
## 2307 0 15.722763 19.60425 17.561628
## 2309 0 15.665611 19.75859 17.595899
## 2311 0 15.599953 19.91694 17.630238
## 2313 0 15.517456 20.08118 17.664643
## 2315 0 15.446045 20.23426 17.699115
## 2317 0 15.356553 20.41402 17.733655
## 2319 0 15.273920 20.61788 17.768262
## 2321 0 15.179424 20.80965 17.802937
## 2323 0 15.076522 21.02060 17.837679
## 2325 0 14.979612 21.25003 17.872490
## 2327 0 14.871893 21.47613 17.907368
## 2329 0 14.770738 21.72285 17.942314
## 2331 0 14.670429 21.93441 17.977328
## 2333 0 14.559271 22.17627 18.012411
## 2335 0 14.456782 22.41026 18.047562
## 2337 0 14.354868 22.69217 18.082782
## 2339 0 14.262584 22.94351 18.118070
## 2341 0 14.167677 23.19956 18.153428
## 2343 0 14.075860 23.46347 18.188854
## 2345 0 13.981751 23.71705 18.224349
## 2347 0 15.786755 19.11063 17.375143
## 2349 0 12.747529 21.42297 16.563946
## 2351 0 12.898402 21.27276 16.596271
## 2353 0 13.044637 21.12472 16.628659
## 2355 0 13.204147 20.96679 16.661109
## 2357 0 13.360318 20.82495 16.693623
## 2359 0 13.509710 20.69745 16.726201
## 2361 0 13.658756 20.55649 16.758842
## 2363 0 13.806695 20.41322 16.791547
## 2365 0 13.953304 20.27007 16.824316
## 2367 0 14.098045 20.13669 16.857148
## 2369 0 14.248390 20.03043 16.890045
## 2371 0 14.391244 19.92344 16.923006
## 2373 0 14.534965 19.81665 16.956031
## 2375 0 14.674231 19.71432 16.989120
## 2377 0 14.801743 19.59719 17.022275
## 2379 0 14.939533 19.48632 17.055494
## 2381 0 15.068288 19.38951 17.088777
## 2383 0 15.188868 19.29975 17.122126
## 2385 0 15.301153 19.23375 17.155540
## 2387 0 15.415208 19.14678 17.189019
## 2389 0 15.510783 19.11594 17.222563
## 2391 0 15.594977 19.07619 17.256173
## 2393 0 15.666168 19.07005 17.289848
## 2395 0 15.727019 19.06893 17.323589
## 2397 0 15.774818 19.08666 17.357396
## 2399 0 15.800921 19.13637 17.391269
## 2401 0 15.808482 19.19543 17.425208
## 2403 0 15.813018 19.26397 17.459213
## 2405 0 15.784327 19.36724 17.493285
## 2407 0 15.759337 19.48890 17.527423
## 2409 0 15.722763 19.60425 17.561628
## 2411 0 15.665611 19.75859 17.595899
## 2413 0 15.599953 19.91694 17.630238
## 2415 0 15.517456 20.08118 17.664643
## 2417 0 15.446045 20.23426 17.699115
## 2419 0 15.356553 20.41402 17.733655
## 2421 0 15.273920 20.61788 17.768262
## 2423 0 15.179424 20.80965 17.802937
## 2425 0 15.076522 21.02060 17.837679
## 2427 0 14.979612 21.25003 17.872490
## 2429 0 14.871893 21.47613 17.907368
## 2431 0 14.770738 21.72285 17.942314
## 2433 0 14.670429 21.93441 17.977328
## 2435 0 14.559271 22.17627 18.012411
## 2437 0 14.456782 22.41026 18.047562
## 2439 0 14.354868 22.69217 18.082782
## 2441 0 14.262584 22.94351 18.118070
## 2443 0 14.167677 23.19956 18.153428
## 2445 0 14.075860 23.46347 18.188854
## 2447 0 13.981751 23.71705 18.224349
## 2449 0 15.786755 19.11063 17.375143
## 2451 0 12.747529 21.42297 16.563946
## 2453 0 12.898402 21.27276 16.596271
## 2455 0 13.044637 21.12472 16.628659
## 2457 0 13.204147 20.96679 16.661109
## 2459 0 13.360318 20.82495 16.693623
## 2461 0 13.509710 20.69745 16.726201
## 2463 0 13.658756 20.55649 16.758842
## 2465 0 13.806695 20.41322 16.791547
## 2467 0 13.953304 20.27007 16.824316
## 2469 0 14.098045 20.13669 16.857148
## 2471 0 14.248390 20.03043 16.890045
## 2473 0 14.391244 19.92344 16.923006
## 2475 0 14.534965 19.81665 16.956031
## 2477 0 14.674231 19.71432 16.989120
## 2479 0 14.801743 19.59719 17.022275
## 2481 0 14.939533 19.48632 17.055494
## 2483 0 15.068288 19.38951 17.088777
## 2485 0 15.188868 19.29975 17.122126
## 2487 0 15.301153 19.23375 17.155540
## 2489 0 15.415208 19.14678 17.189019
## 2491 0 15.510783 19.11594 17.222563
## 2493 0 15.594977 19.07619 17.256173
## 2495 0 15.666168 19.07005 17.289848
## 2497 0 15.727019 19.06893 17.323589
## 2499 0 15.774818 19.08666 17.357396
## 2501 0 15.800921 19.13637 17.391269
## 2503 0 15.808482 19.19543 17.425208
## 2505 0 15.813018 19.26397 17.459213
## 2507 0 15.784327 19.36724 17.493285
## 2509 0 15.759337 19.48890 17.527423
## 2511 0 15.722763 19.60425 17.561628
## 2513 0 15.665611 19.75859 17.595899
## 2515 0 15.599953 19.91694 17.630238
## 2517 0 15.517456 20.08118 17.664643
## 2519 0 15.446045 20.23426 17.699115
## 2521 0 15.356553 20.41402 17.733655
## 2523 0 15.273920 20.61788 17.768262
## 2525 0 15.179424 20.80965 17.802937
## 2527 0 15.076522 21.02060 17.837679
## 2529 0 14.979612 21.25003 17.872490
## 2531 0 14.871893 21.47613 17.907368
## 2533 0 14.770738 21.72285 17.942314
## 2535 0 14.670429 21.93441 17.977328
## 2537 0 14.559271 22.17627 18.012411
## 2539 0 14.456782 22.41026 18.047562
## 2541 0 14.354868 22.69217 18.082782
## 2543 0 14.262584 22.94351 18.118070
## 2545 0 14.167677 23.19956 18.153428
## 2547 0 14.075860 23.46347 18.188854
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## 4241 0 15.784327 19.36724 17.493285
## 4243 0 15.759337 19.48890 17.527423
## 4245 0 15.722763 19.60425 17.561628
## 4247 0 15.665611 19.75859 17.595899
## 4249 0 15.599953 19.91694 17.630238
## 4251 0 15.517456 20.08118 17.664643
## 4253 0 15.446045 20.23426 17.699115
## 4255 0 15.356553 20.41402 17.733655
## 4257 0 15.273920 20.61788 17.768262
## 4259 0 15.179424 20.80965 17.802937
## 4261 0 15.076522 21.02060 17.837679
## 4263 0 14.979612 21.25003 17.872490
## 4265 0 14.871893 21.47613 17.907368
## 4267 0 14.770738 21.72285 17.942314
## 4269 0 14.670429 21.93441 17.977328
## 4271 0 14.559271 22.17627 18.012411
## 4273 0 14.456782 22.41026 18.047562
## 4275 0 14.354868 22.69217 18.082782
## 4277 0 14.262584 22.94351 18.118070
## 4279 0 14.167677 23.19956 18.153428
## 4281 0 14.075860 23.46347 18.188854
## 4283 0 13.981751 23.71705 18.224349
## 4285 0 15.786755 19.11063 17.375143
## 4287 0 12.747529 21.42297 16.563946
## 4289 0 12.898402 21.27276 16.596271
## 4291 0 13.044637 21.12472 16.628659
## 4293 0 13.204147 20.96679 16.661109
## 4295 0 13.360318 20.82495 16.693623
## 4297 0 13.509710 20.69745 16.726201
## 4299 0 13.658756 20.55649 16.758842
## 4301 0 13.806695 20.41322 16.791547
## 4303 0 13.953304 20.27007 16.824316
## 4305 0 14.098045 20.13669 16.857148
## 4307 0 14.248390 20.03043 16.890045
## 4309 0 14.391244 19.92344 16.923006
## 4311 0 14.534965 19.81665 16.956031
## 4313 0 14.674231 19.71432 16.989120
## 4315 0 14.801743 19.59719 17.022275
## 4317 0 14.939533 19.48632 17.055494
## 4319 0 15.068288 19.38951 17.088777
## 4321 0 15.188868 19.29975 17.122126
## 4323 0 15.301153 19.23375 17.155540
## 4325 0 15.415208 19.14678 17.189019
## 4327 0 15.510783 19.11594 17.222563
## 4329 0 15.594977 19.07619 17.256173
## 4331 0 15.666168 19.07005 17.289848
## 4333 0 15.727019 19.06893 17.323589
## 4335 0 15.774818 19.08666 17.357396
## 4337 0 15.800921 19.13637 17.391269
## 4339 0 15.808482 19.19543 17.425208
## 4341 0 15.813018 19.26397 17.459213
## 4343 0 15.784327 19.36724 17.493285
## 4345 0 15.759337 19.48890 17.527423
## 4347 0 15.722763 19.60425 17.561628
## 4349 0 15.665611 19.75859 17.595899
## 4351 0 15.599953 19.91694 17.630238
## 4353 0 15.517456 20.08118 17.664643
## 4355 0 15.446045 20.23426 17.699115
## 4357 0 15.356553 20.41402 17.733655
## 4359 0 15.273920 20.61788 17.768262
## 4361 0 15.179424 20.80965 17.802937
## 4363 0 15.076522 21.02060 17.837679
## 4365 0 14.979612 21.25003 17.872490
## 4367 0 14.871893 21.47613 17.907368
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## 4371 0 14.670429 21.93441 17.977328
## 4373 0 14.559271 22.17627 18.012411
## 4375 0 14.456782 22.41026 18.047562
## 4377 0 14.354868 22.69217 18.082782
## 4379 0 14.262584 22.94351 18.118070
## 4381 0 14.167677 23.19956 18.153428
## 4383 0 14.075860 23.46347 18.188854
## 4385 0 13.981751 23.71705 18.224349
## 4387 0 15.786755 19.11063 17.375143
## 4389 0 12.747529 21.42297 16.563946
## 4391 0 12.898402 21.27276 16.596271
## 4393 0 13.044637 21.12472 16.628659
## 4395 0 13.204147 20.96679 16.661109
## 4397 0 13.360318 20.82495 16.693623
## 4399 0 13.509710 20.69745 16.726201
## 4401 0 13.658756 20.55649 16.758842
## 4403 0 13.806695 20.41322 16.791547
## 4405 0 13.953304 20.27007 16.824316
## 4407 0 14.098045 20.13669 16.857148
## 4409 0 14.248390 20.03043 16.890045
## 4411 0 14.391244 19.92344 16.923006
## 4413 0 14.534965 19.81665 16.956031
## 4415 0 14.674231 19.71432 16.989120
## 4417 0 14.801743 19.59719 17.022275
## 4419 0 14.939533 19.48632 17.055494
## 4421 0 15.068288 19.38951 17.088777
## 4423 0 15.188868 19.29975 17.122126
## 4425 0 15.301153 19.23375 17.155540
## 4427 0 15.415208 19.14678 17.189019
## 4429 0 15.510783 19.11594 17.222563
## 4431 0 15.594977 19.07619 17.256173
## 4433 0 15.666168 19.07005 17.289848
## 4435 0 15.727019 19.06893 17.323589
## 4437 0 15.774818 19.08666 17.357396
## 4439 0 15.800921 19.13637 17.391269
## 4441 0 15.808482 19.19543 17.425208
## 4443 0 15.813018 19.26397 17.459213
## 4445 0 15.784327 19.36724 17.493285
## 4447 0 15.759337 19.48890 17.527423
## 4449 0 15.722763 19.60425 17.561628
## 4451 0 15.665611 19.75859 17.595899
## 4453 0 15.599953 19.91694 17.630238
## 4455 0 15.517456 20.08118 17.664643
## 4457 0 15.446045 20.23426 17.699115
## 4459 0 15.356553 20.41402 17.733655
## 4461 0 15.273920 20.61788 17.768262
## 4463 0 15.179424 20.80965 17.802937
## 4465 0 15.076522 21.02060 17.837679
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## 4469 0 14.871893 21.47613 17.907368
## 4471 0 14.770738 21.72285 17.942314
## 4473 0 14.670429 21.93441 17.977328
## 4475 0 14.559271 22.17627 18.012411
## 4477 0 14.456782 22.41026 18.047562
## 4479 0 14.354868 22.69217 18.082782
## 4481 0 14.262584 22.94351 18.118070
## 4483 0 14.167677 23.19956 18.153428
## 4485 0 14.075860 23.46347 18.188854
## 4487 0 13.981751 23.71705 18.224349
## 4489 0 15.786755 19.11063 17.375143
## 4491 0 12.747529 21.42297 16.563946
## 4493 0 12.898402 21.27276 16.596271
## 4495 0 13.044637 21.12472 16.628659
## 4497 0 13.204147 20.96679 16.661109
## 4499 0 13.360318 20.82495 16.693623
## 4501 0 13.509710 20.69745 16.726201
## 4503 0 13.658756 20.55649 16.758842
## 4505 0 13.806695 20.41322 16.791547
## 4507 0 13.953304 20.27007 16.824316
## 4509 0 14.098045 20.13669 16.857148
## 4511 0 14.248390 20.03043 16.890045
## 4513 0 14.391244 19.92344 16.923006
## 4515 0 14.534965 19.81665 16.956031
## 4517 0 14.674231 19.71432 16.989120
## 4519 0 14.801743 19.59719 17.022275
## 4521 0 14.939533 19.48632 17.055494
## 4523 0 15.068288 19.38951 17.088777
## 4525 0 15.188868 19.29975 17.122126
## 4527 0 15.301153 19.23375 17.155540
## 4529 0 15.415208 19.14678 17.189019
## 4531 0 15.510783 19.11594 17.222563
## 4533 0 15.594977 19.07619 17.256173
## 4535 0 15.666168 19.07005 17.289848
## 4537 0 15.727019 19.06893 17.323589
## 4539 0 15.774818 19.08666 17.357396
## 4541 0 15.800921 19.13637 17.391269
## 4543 0 15.808482 19.19543 17.425208
## 4545 0 15.813018 19.26397 17.459213
## 4547 0 15.784327 19.36724 17.493285
## 4549 0 15.759337 19.48890 17.527423
## 4551 0 15.722763 19.60425 17.561628
## 4553 0 15.665611 19.75859 17.595899
## 4555 0 15.599953 19.91694 17.630238
## 4557 0 15.517456 20.08118 17.664643
## 4559 0 15.446045 20.23426 17.699115
## 4561 0 15.356553 20.41402 17.733655
## 4563 0 15.273920 20.61788 17.768262
## 4565 0 15.179424 20.80965 17.802937
## 4567 0 15.076522 21.02060 17.837679
## 4569 0 14.979612 21.25003 17.872490
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## 4575 0 14.670429 21.93441 17.977328
## 4577 0 14.559271 22.17627 18.012411
## 4579 0 14.456782 22.41026 18.047562
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## 4583 0 14.262584 22.94351 18.118070
## 4585 0 14.167677 23.19956 18.153428
## 4587 0 14.075860 23.46347 18.188854
## 4589 0 13.981751 23.71705 18.224349
## 4591 0 15.786755 19.11063 17.375143
## 4593 0 12.747529 21.42297 16.563946
## 4595 0 12.898402 21.27276 16.596271
## 4597 0 13.044637 21.12472 16.628659
## 4599 0 13.204147 20.96679 16.661109
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## 4603 0 13.509710 20.69745 16.726201
## 4605 0 13.658756 20.55649 16.758842
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## 4609 0 13.953304 20.27007 16.824316
## 4611 0 14.098045 20.13669 16.857148
## 4613 0 14.248390 20.03043 16.890045
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## 4617 0 14.534965 19.81665 16.956031
## 4619 0 14.674231 19.71432 16.989120
## 4621 0 14.801743 19.59719 17.022275
## 4623 0 14.939533 19.48632 17.055494
## 4625 0 15.068288 19.38951 17.088777
## 4627 0 15.188868 19.29975 17.122126
## 4629 0 15.301153 19.23375 17.155540
## 4631 0 15.415208 19.14678 17.189019
## 4633 0 15.510783 19.11594 17.222563
## 4635 0 15.594977 19.07619 17.256173
## 4637 0 15.666168 19.07005 17.289848
## 4639 0 15.727019 19.06893 17.323589
## 4641 0 15.774818 19.08666 17.357396
## 4643 0 15.800921 19.13637 17.391269
## 4645 0 15.808482 19.19543 17.425208
## 4647 0 15.813018 19.26397 17.459213
## 4649 0 15.784327 19.36724 17.493285
## 4651 0 15.759337 19.48890 17.527423
## 4653 0 15.722763 19.60425 17.561628
## 4655 0 15.665611 19.75859 17.595899
## 4657 0 15.599953 19.91694 17.630238
## 4659 0 15.517456 20.08118 17.664643
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## 4663 0 15.356553 20.41402 17.733655
## 4665 0 15.273920 20.61788 17.768262
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## 4669 0 15.076522 21.02060 17.837679
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## 4677 0 14.670429 21.93441 17.977328
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## 4687 0 14.167677 23.19956 18.153428
## 4689 0 14.075860 23.46347 18.188854
## 4691 0 13.981751 23.71705 18.224349
## 4693 0 15.786755 19.11063 17.375143
## 4695 0 12.747529 21.42297 16.563946
## 4697 0 12.898402 21.27276 16.596271
## 4699 0 13.044637 21.12472 16.628659
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## 4719 0 14.534965 19.81665 16.956031
## 4721 0 14.674231 19.71432 16.989120
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## 4727 0 15.068288 19.38951 17.088777
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## 4733 0 15.415208 19.14678 17.189019
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## 4737 0 15.594977 19.07619 17.256173
## 4739 0 15.666168 19.07005 17.289848
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## 4743 0 15.774818 19.08666 17.357396
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## 4753 0 15.759337 19.48890 17.527423
## 4755 0 15.722763 19.60425 17.561628
## 4757 0 15.665611 19.75859 17.595899
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## 4789 0 14.167677 23.19956 18.153428
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## 4793 0 13.981751 23.71705 18.224349
## 4795 0 15.786755 19.11063 17.375143
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## 4799 0 12.898402 21.27276 16.596271
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## 4823 0 14.674231 19.71432 16.989120
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## 4829 0 15.068288 19.38951 17.088777
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## 4835 0 15.415208 19.14678 17.189019
## 4837 0 15.510783 19.11594 17.222563
## 4839 0 15.594977 19.07619 17.256173
## 4841 0 15.666168 19.07005 17.289848
## 4843 0 15.727019 19.06893 17.323589
## 4845 0 15.774818 19.08666 17.357396
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## 4849 0 15.808482 19.19543 17.425208
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## 4853 0 15.784327 19.36724 17.493285
## 4855 0 15.759337 19.48890 17.527423
## 4857 0 15.722763 19.60425 17.561628
## 4859 0 15.665611 19.75859 17.595899
## 4861 0 15.599953 19.91694 17.630238
## 4863 0 15.517456 20.08118 17.664643
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## 4891 0 14.167677 23.19956 18.153428
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## 4895 0 13.981751 23.71705 18.224349
## 4897 0 15.786755 19.11063 17.375143
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## 4925 0 14.674231 19.71432 16.989120
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## 4943 0 15.666168 19.07005 17.289848
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## 4955 0 15.784327 19.36724 17.493285
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## 5027 0 14.674231 19.71432 16.989120
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## 5033 0 15.068288 19.38951 17.088777
## 5035 0 15.188868 19.29975 17.122126
## 5037 0 15.301153 19.23375 17.155540
## 5039 0 15.415208 19.14678 17.189019
## 5041 0 15.510783 19.11594 17.222563
## 5043 0 15.594977 19.07619 17.256173
## 5045 0 15.666168 19.07005 17.289848
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## 5049 0 15.774818 19.08666 17.357396
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## 5053 0 15.808482 19.19543 17.425208
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## 5057 0 15.784327 19.36724 17.493285
## 5059 0 15.759337 19.48890 17.527423
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## 5083 0 14.770738 21.72285 17.942314
## 5085 0 14.670429 21.93441 17.977328
## 5087 0 14.559271 22.17627 18.012411
## 5089 0 14.456782 22.41026 18.047562
## 5091 0 14.354868 22.69217 18.082782
## 5093 0 14.262584 22.94351 18.118070
## 5095 0 14.167677 23.19956 18.153428
## 5097 0 14.075860 23.46347 18.188854
## 5099 0 13.981751 23.71705 18.224349
## 5204 0 15.786755 19.11063 17.375143
## 5206 0 12.747529 21.42297 16.563946
## 5208 0 12.898402 21.27276 16.596271
## 5210 0 13.044637 21.12472 16.628659
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## 5216 0 13.509710 20.69745 16.726201
## 5218 0 13.658756 20.55649 16.758842
## 5220 0 13.806695 20.41322 16.791547
## 5222 0 13.953304 20.27007 16.824316
## 5224 0 14.098045 20.13669 16.857148
## 5226 0 14.248390 20.03043 16.890045
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## 5230 0 14.534965 19.81665 16.956031
## 5232 0 14.674231 19.71432 16.989120
## 5234 0 14.801743 19.59719 17.022275
## 5236 0 14.939533 19.48632 17.055494
## 5238 0 15.068288 19.38951 17.088777
## 5240 0 15.188868 19.29975 17.122126
## 5242 0 15.301153 19.23375 17.155540
## 5244 0 15.415208 19.14678 17.189019
## 5246 0 15.510783 19.11594 17.222563
## 5248 0 15.594977 19.07619 17.256173
## 5250 0 15.666168 19.07005 17.289848
## 5252 0 15.727019 19.06893 17.323589
## 5254 0 15.774818 19.08666 17.357396
## 5256 0 15.800921 19.13637 17.391269
## 5258 0 15.808482 19.19543 17.425208
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## 5262 0 15.784327 19.36724 17.493285
## 5264 0 15.759337 19.48890 17.527423
## 5266 0 15.722763 19.60425 17.561628
## 5268 0 15.665611 19.75859 17.595899
## 5270 0 15.599953 19.91694 17.630238
## 5272 0 15.517456 20.08118 17.664643
## 5274 0 15.446045 20.23426 17.699115
## 5276 0 15.356553 20.41402 17.733655
## 5278 0 15.273920 20.61788 17.768262
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## 5282 0 15.076522 21.02060 17.837679
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## 5286 0 14.871893 21.47613 17.907368
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## 5290 0 14.670429 21.93441 17.977328
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## 5298 0 14.262584 22.94351 18.118070
## 5300 0 14.167677 23.19956 18.153428
## 5302 0 14.075860 23.46347 18.188854
## 5304 0 13.981751 23.71705 18.224349
## 5306 0 15.786755 19.11063 17.375143
## 5308 0 12.747529 21.42297 16.563946
## 5310 0 12.898402 21.27276 16.596271
## 5312 0 13.044637 21.12472 16.628659
## 5314 0 13.204147 20.96679 16.661109
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## 5318 0 13.509710 20.69745 16.726201
## 5320 0 13.658756 20.55649 16.758842
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## 5324 0 13.953304 20.27007 16.824316
## 5326 0 14.098045 20.13669 16.857148
## 5328 0 14.248390 20.03043 16.890045
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## 5332 0 14.534965 19.81665 16.956031
## 5334 0 14.674231 19.71432 16.989120
## 5336 0 14.801743 19.59719 17.022275
## 5338 0 14.939533 19.48632 17.055494
## 5340 0 15.068288 19.38951 17.088777
## 5342 0 15.188868 19.29975 17.122126
## 5344 0 15.301153 19.23375 17.155540
## 5346 0 15.415208 19.14678 17.189019
## 5348 0 15.510783 19.11594 17.222563
## 5350 0 15.594977 19.07619 17.256173
## 5352 0 15.666168 19.07005 17.289848
## 5354 0 15.727019 19.06893 17.323589
## 5356 0 15.774818 19.08666 17.357396
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## 5360 0 15.808482 19.19543 17.425208
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## 5364 0 15.784327 19.36724 17.493285
## 5366 0 15.759337 19.48890 17.527423
## 5368 0 15.722763 19.60425 17.561628
## 5370 0 15.665611 19.75859 17.595899
## 5372 0 15.599953 19.91694 17.630238
## 5374 0 15.517456 20.08118 17.664643
## 5376 0 15.446045 20.23426 17.699115
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## 5380 0 15.273920 20.61788 17.768262
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## 5384 0 15.076522 21.02060 17.837679
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## 5388 0 14.871893 21.47613 17.907368
## 5390 0 14.770738 21.72285 17.942314
## 5392 0 14.670429 21.93441 17.977328
## 5394 0 14.559271 22.17627 18.012411
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## 5400 0 14.262584 22.94351 18.118070
## 5402 0 14.167677 23.19956 18.153428
## 5404 0 14.075860 23.46347 18.188854
## 5406 0 13.981751 23.71705 18.224349
## 5408 0 15.786755 19.11063 17.375143
## 5410 0 12.747529 21.42297 16.563946
## 5412 0 12.898402 21.27276 16.596271
## 5414 0 13.044637 21.12472 16.628659
## 5416 0 13.204147 20.96679 16.661109
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## 5420 0 13.509710 20.69745 16.726201
## 5422 0 13.658756 20.55649 16.758842
## 5424 0 13.806695 20.41322 16.791547
## 5426 0 13.953304 20.27007 16.824316
## 5428 0 14.098045 20.13669 16.857148
## 5430 0 14.248390 20.03043 16.890045
## 5432 0 14.391244 19.92344 16.923006
## 5434 0 14.534965 19.81665 16.956031
## 5436 0 14.674231 19.71432 16.989120
## 5438 0 14.801743 19.59719 17.022275
## 5440 0 14.939533 19.48632 17.055494
## 5442 0 15.068288 19.38951 17.088777
## 5444 0 15.188868 19.29975 17.122126
## 5446 0 15.301153 19.23375 17.155540
## 5448 0 15.415208 19.14678 17.189019
## 5450 0 15.510783 19.11594 17.222563
## 5452 0 15.594977 19.07619 17.256173
## 5454 0 15.666168 19.07005 17.289848
## 5456 0 15.727019 19.06893 17.323589
## 5458 0 15.774818 19.08666 17.357396
## 5460 0 15.800921 19.13637 17.391269
## 5462 0 15.808482 19.19543 17.425208
## 5464 0 15.813018 19.26397 17.459213
## 5466 0 15.784327 19.36724 17.493285
## 5468 0 15.759337 19.48890 17.527423
## 5470 0 15.722763 19.60425 17.561628
## 5472 0 15.665611 19.75859 17.595899
## 5474 0 15.599953 19.91694 17.630238
## 5476 0 15.517456 20.08118 17.664643
## 5478 0 15.446045 20.23426 17.699115
## 5480 0 15.356553 20.41402 17.733655
## 5482 0 15.273920 20.61788 17.768262
## 5484 0 15.179424 20.80965 17.802937
## 5486 0 15.076522 21.02060 17.837679
## 5488 0 14.979612 21.25003 17.872490
## 5490 0 14.871893 21.47613 17.907368
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## 5494 0 14.670429 21.93441 17.977328
## 5496 0 14.559271 22.17627 18.012411
## 5498 0 14.456782 22.41026 18.047562
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## 5502 0 14.262584 22.94351 18.118070
## 5504 0 14.167677 23.19956 18.153428
## 5506 0 14.075860 23.46347 18.188854
## 5508 0 13.981751 23.71705 18.224349
## 5510 0 15.786755 19.11063 17.375143
## 5512 0 12.747529 21.42297 16.563946
## 5514 0 12.898402 21.27276 16.596271
## 5516 0 13.044637 21.12472 16.628659
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## 5520 0 13.360318 20.82495 16.693623
## 5522 0 13.509710 20.69745 16.726201
## 5524 0 13.658756 20.55649 16.758842
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## 5528 0 13.953304 20.27007 16.824316
## 5530 0 14.098045 20.13669 16.857148
## 5532 0 14.248390 20.03043 16.890045
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## 5536 0 14.534965 19.81665 16.956031
## 5538 0 14.674231 19.71432 16.989120
## 5540 0 14.801743 19.59719 17.022275
## 5542 0 14.939533 19.48632 17.055494
## 5544 0 15.068288 19.38951 17.088777
## 5546 0 15.188868 19.29975 17.122126
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## 5550 0 15.415208 19.14678 17.189019
## 5552 0 15.510783 19.11594 17.222563
## 5554 0 15.594977 19.07619 17.256173
## 5556 0 15.666168 19.07005 17.289848
## 5558 0 15.727019 19.06893 17.323589
## 5560 0 15.774818 19.08666 17.357396
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## 5564 0 15.808482 19.19543 17.425208
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## 5568 0 15.784327 19.36724 17.493285
## 5570 0 15.759337 19.48890 17.527423
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## 5574 0 15.665611 19.75859 17.595899
## 5576 0 15.599953 19.91694 17.630238
## 5578 0 15.517456 20.08118 17.664643
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## 5584 0 15.273920 20.61788 17.768262
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## 5588 0 15.076522 21.02060 17.837679
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## 5594 0 14.770738 21.72285 17.942314
## 5596 0 14.670429 21.93441 17.977328
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## 5604 0 14.262584 22.94351 18.118070
## 5606 0 14.167677 23.19956 18.153428
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## 5610 0 13.981751 23.71705 18.224349
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## 5616 0 12.898402 21.27276 16.596271
## 5618 0 13.044637 21.12472 16.628659
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## 5640 0 14.674231 19.71432 16.989120
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## 5646 0 15.068288 19.38951 17.088777
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## 5652 0 15.415208 19.14678 17.189019
## 5654 0 15.510783 19.11594 17.222563
## 5656 0 15.594977 19.07619 17.256173
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## 5662 0 15.774818 19.08666 17.357396
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## 5666 0 15.808482 19.19543 17.425208
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## 5674 0 15.722763 19.60425 17.561628
## 5676 0 15.665611 19.75859 17.595899
## 5678 0 15.599953 19.91694 17.630238
## 5680 0 15.517456 20.08118 17.664643
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## 5686 0 15.273920 20.61788 17.768262
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## 5754 0 15.415208 19.14678 17.189019
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## 5778 0 15.665611 19.75859 17.595899
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## 5820 0 12.898402 21.27276 16.596271
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## 5844 0 14.674231 19.71432 16.989120
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## 5850 0 15.068288 19.38951 17.088777
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## 5856 0 15.415208 19.14678 17.189019
## 5858 0 15.510783 19.11594 17.222563
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## 5862 0 15.666168 19.07005 17.289848
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## 5874 0 15.784327 19.36724 17.493285
## 5876 0 15.759337 19.48890 17.527423
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## 5884 0 15.517456 20.08118 17.664643
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## 5894 0 15.076522 21.02060 17.837679
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## 5912 0 14.167677 23.19956 18.153428
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## 5918 0 15.786755 19.11063 17.375143
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## 5922 0 12.898402 21.27276 16.596271
## 5924 0 13.044637 21.12472 16.628659
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## 5944 0 14.534965 19.81665 16.956031
## 5946 0 14.674231 19.71432 16.989120
## 5948 0 14.801743 19.59719 17.022275
## 5950 0 14.939533 19.48632 17.055494
## 5952 0 15.068288 19.38951 17.088777
## 5954 0 15.188868 19.29975 17.122126
## 5956 0 15.301153 19.23375 17.155540
## 5958 0 15.415208 19.14678 17.189019
## 5960 0 15.510783 19.11594 17.222563
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## 5968 0 15.774818 19.08666 17.357396
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## 5972 0 15.808482 19.19543 17.425208
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## 5976 0 15.784327 19.36724 17.493285
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## 5982 0 15.665611 19.75859 17.595899
## 5984 0 15.599953 19.91694 17.630238
## 5986 0 15.517456 20.08118 17.664643
## 5988 0 15.446045 20.23426 17.699115
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## 5992 0 15.273920 20.61788 17.768262
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## 5996 0 15.076522 21.02060 17.837679
## 5998 0 14.979612 21.25003 17.872490
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## 6012 0 14.262584 22.94351 18.118070
## 6014 0 14.167677 23.19956 18.153428
## 6016 0 14.075860 23.46347 18.188854
## 6018 0 13.981751 23.71705 18.224349
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## 6024 0 12.898402 21.27276 16.596271
## 6026 0 13.044637 21.12472 16.628659
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## 6030 0 13.360318 20.82495 16.693623
## 6032 0 13.509710 20.69745 16.726201
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## 8774 0 15.786755 19.11063 17.375143
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## 8778 0 12.898402 21.27276 16.596271
## 8780 0 13.044637 21.12472 16.628659
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## 8804 0 14.801743 19.59719 17.022275
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## 8820 0 15.666168 19.07005 17.289848
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## 8830 0 15.813018 19.26397 17.459213
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## 8876 0 15.786755 19.11063 17.375143
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## 8882 0 13.044637 21.12472 16.628659
## 8884 0 13.204147 20.96679 16.661109
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## 8888 0 13.509710 20.69745 16.726201
## 8890 0 13.658756 20.55649 16.758842
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## 8898 0 14.248390 20.03043 16.890045
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## 8984 0 13.044637 21.12472 16.628659
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## 9416 0 14.801743 19.59719 17.022275
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## 11960 0 9.286074 12.80889 10.908379
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## 12002 0 12.830995 16.26985 14.463305
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## 12006 0 13.029273 16.92409 14.857129
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## 12014 0 13.353466 18.42843 15.677241
## 12016 0 13.432372 18.82567 15.889247
## 12018 0 13.513453 19.23936 16.104120
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## 12034 0 14.012368 22.99509 17.931080
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## 12038 0 11.884939 14.34782 13.081450
## 12040 0 7.278795 12.16782 9.410003
## 12042 0 7.442278 12.22654 9.537256
## 12044 0 7.616903 12.27506 9.666230
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## 12108 0 13.029273 16.92409 14.857129
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## 12116 0 13.353466 18.42843 15.677241
## 12118 0 13.432372 18.82567 15.889247
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## 12126 0 13.688893 20.55819 16.766331
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## 12132 0 13.889533 22.00975 17.455773
## 12134 0 13.954464 22.51002 17.691830
## 12136 0 14.012368 22.99509 17.931080
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## 12140 0 11.884939 14.34782 13.081450
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## 12144 0 7.442278 12.22654 9.537256
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## 12164 0 9.286074 12.80889 10.908379
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## 12170 0 9.898005 13.03710 11.356939
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## 12182 0 11.084090 13.63597 12.310151
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## 12188 0 11.639194 14.08734 12.816351
## 12190 0 11.802069 14.25588 12.989669
## 12192 0 11.954662 14.44565 13.165331
## 12194 0 12.095975 14.67114 13.343368
## 12196 0 12.245470 14.88313 13.523812
## 12198 0 12.384249 15.12745 13.706697
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## 12202 0 12.617263 15.66209 14.079920
## 12204 0 12.729714 15.96001 14.270325
## 12206 0 12.830995 16.26985 14.463305
## 12208 0 12.933504 16.58753 14.658895
## 12210 0 13.029273 16.92409 14.857129
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## 12214 0 13.188133 17.64512 15.261677
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## 12218 0 13.353466 18.42843 15.677241
## 12220 0 13.432372 18.82567 15.889247
## 12222 0 13.513453 19.23936 16.104120
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## 12228 0 13.688893 20.55819 16.766331
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## 12234 0 13.889533 22.00975 17.455773
## 12236 0 13.954464 22.51002 17.691830
## 12238 0 14.012368 22.99509 17.931080
## 12240 0 14.071917 23.51784 18.173565
## 12242 0 11.884939 14.34782 13.081450
## 12244 0 7.278795 12.16782 9.410003
## 12246 0 7.442278 12.22654 9.537256
## 12248 0 7.616903 12.27506 9.666230
## 12250 0 7.794476 12.33184 9.796948
## 12252 0 7.968878 12.37636 9.929433
## 12254 0 8.156875 12.43860 10.063711
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## 12266 0 9.286074 12.80889 10.908379
## 12268 0 9.482701 12.88412 11.055895
## 12270 0 9.688510 12.95809 11.205406
## 12272 0 9.898005 13.03710 11.356939
## 12274 0 10.093741 13.13322 11.510520
## 12276 0 10.295404 13.21189 11.666179
## 12278 0 10.487528 13.31396 11.823943
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## 12284 0 11.084090 13.63597 12.310151
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## 12288 0 11.452446 13.92574 12.645346
## 12290 0 11.639194 14.08734 12.816351
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## 12294 0 11.954662 14.44565 13.165331
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## 12298 0 12.245470 14.88313 13.523812
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## 12312 0 13.029273 16.92409 14.857129
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## 12340 0 14.012368 22.99509 17.931080
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## 12344 0 11.884939 14.34782 13.081450
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## 12348 0 7.442278 12.22654 9.537256
## 12350 0 7.616903 12.27506 9.666230
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## 12368 0 9.286074 12.80889 10.908379
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## 12374 0 9.898005 13.03710 11.356939
## 12376 0 10.093741 13.13322 11.510520
## 12378 0 10.295404 13.21189 11.666179
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## 12422 0 13.353466 18.42843 15.677241
## 12424 0 13.432372 18.82567 15.889247
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## 12442 0 14.012368 22.99509 17.931080
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## 12446 0 11.884939 14.34782 13.081450
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## 12452 0 7.616903 12.27506 9.666230
## 12454 0 7.794476 12.33184 9.796948
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## 12470 0 9.286074 12.80889 10.908379
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## 12478 0 10.093741 13.13322 11.510520
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## 12494 0 11.639194 14.08734 12.816351
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## 12504 0 12.384249 15.12745 13.706697
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## 12516 0 13.029273 16.92409 14.857129
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## 12526 0 13.432372 18.82567 15.889247
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## 12544 0 14.012368 22.99509 17.931080
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## 12548 0 11.884939 14.34782 13.081450
## 12550 0 7.278795 12.16782 9.410003
## 12552 0 7.442278 12.22654 9.537256
## 12554 0 7.616903 12.27506 9.666230
## 12556 0 7.794476 12.33184 9.796948
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## 12562 0 8.340492 12.49641 10.199804
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## 12572 0 9.286074 12.80889 10.908379
## 12574 0 9.482701 12.88412 11.055895
## 12576 0 9.688510 12.95809 11.205406
## 12578 0 9.898005 13.03710 11.356939
## 12580 0 10.093741 13.13322 11.510520
## 12582 0 10.295404 13.21189 11.666179
## 12584 0 10.487528 13.31396 11.823943
## 12586 0 10.688480 13.41519 11.983840
## 12588 0 10.884731 13.51431 12.145900
## 12590 0 11.084090 13.63597 12.310151
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## 12594 0 11.452446 13.92574 12.645346
## 12596 0 11.639194 14.08734 12.816351
## 12598 0 11.802069 14.25588 12.989669
## 12600 0 11.954662 14.44565 13.165331
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## 12604 0 12.245470 14.88313 13.523812
## 12606 0 12.384249 15.12745 13.706697
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## 12612 0 12.729714 15.96001 14.270325
## 12614 0 12.830995 16.26985 14.463305
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## 12618 0 13.029273 16.92409 14.857129
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## 12622 0 13.188133 17.64512 15.261677
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## 12626 0 13.353466 18.42843 15.677241
## 12628 0 13.432372 18.82567 15.889247
## 12630 0 13.513453 19.23936 16.104120
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## 12644 0 13.954464 22.51002 17.691830
## 12646 0 14.012368 22.99509 17.931080
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## 12650 0 11.884939 14.34782 13.081450
## 12652 0 7.278795 12.16782 9.410003
## 12654 0 7.442278 12.22654 9.537256
## 12656 0 7.616903 12.27506 9.666230
## 12658 0 7.794476 12.33184 9.796948
## 12660 0 7.968878 12.37636 9.929433
## 12662 0 8.156875 12.43860 10.063711
## 12664 0 8.340492 12.49641 10.199804
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## 12670 0 8.897316 12.69166 10.619226
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## 12674 0 9.286074 12.80889 10.908379
## 12676 0 9.482701 12.88412 11.055895
## 12678 0 9.688510 12.95809 11.205406
## 12680 0 9.898005 13.03710 11.356939
## 12682 0 10.093741 13.13322 11.510520
## 12684 0 10.295404 13.21189 11.666179
## 12686 0 10.487528 13.31396 11.823943
## 12688 0 10.688480 13.41519 11.983840
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## 12692 0 11.084090 13.63597 12.310151
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## 12696 0 11.452446 13.92574 12.645346
## 12698 0 11.639194 14.08734 12.816351
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## 12702 0 11.954662 14.44565 13.165331
## 12704 0 12.095975 14.67114 13.343368
## 12706 0 12.245470 14.88313 13.523812
## 12708 0 12.384249 15.12745 13.706697
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## 12716 0 12.830995 16.26985 14.463305
## 12718 0 12.933504 16.58753 14.658895
## 12720 0 13.029273 16.92409 14.857129
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## 12724 0 13.188133 17.64512 15.261677
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## 12728 0 13.353466 18.42843 15.677241
## 12730 0 13.432372 18.82567 15.889247
## 12732 0 13.513453 19.23936 16.104120
## 12734 0 13.582972 19.67060 16.321898
## 12736 0 13.633575 20.10565 16.542622
## 12738 0 13.688893 20.55819 16.766331
## 12740 0 13.756667 21.01867 16.993065
## 12742 0 13.814921 21.49962 17.222865
## 12744 0 13.889533 22.00975 17.455773
## 12746 0 13.954464 22.51002 17.691830
## 12748 0 14.012368 22.99509 17.931080
## 12750 0 14.071917 23.51784 18.173565
## 12752 0 11.884939 14.34782 13.081450
## 12754 0 7.278795 12.16782 9.410003
## 12756 0 7.442278 12.22654 9.537256
## 12758 0 7.616903 12.27506 9.666230
## 12760 0 7.794476 12.33184 9.796948
## 12762 0 7.968878 12.37636 9.929433
## 12764 0 8.156875 12.43860 10.063711
## 12766 0 8.340492 12.49641 10.199804
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## 12770 0 8.708284 12.62582 10.477537
## 12772 0 8.897316 12.69166 10.619226
## 12774 0 9.089560 12.74577 10.762832
## 12776 0 9.286074 12.80889 10.908379
## 12778 0 9.482701 12.88412 11.055895
## 12780 0 9.688510 12.95809 11.205406
## 12782 0 9.898005 13.03710 11.356939
## 12784 0 10.093741 13.13322 11.510520
## 12786 0 10.295404 13.21189 11.666179
## 12788 0 10.487528 13.31396 11.823943
## 12790 0 10.688480 13.41519 11.983840
## 12792 0 10.884731 13.51431 12.145900
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## 15583 0 13.353466 18.42843 15.677241
## 15585 0 13.432372 18.82567 15.889247
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## 15603 0 14.012368 22.99509 17.931080
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## 15609 0 7.278795 12.16782 9.410003
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## 15631 0 9.286074 12.80889 10.908379
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## 15677 0 13.029273 16.92409 14.857129
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## 15681 0 13.188133 17.64512 15.261677
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## 15685 0 13.353466 18.42843 15.677241
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## 15689 0 13.513453 19.23936 16.104120
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## 15705 0 14.012368 22.99509 17.931080
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## 15709 0 11.884939 14.34782 13.081450
## 15711 0 7.278795 12.16782 9.410003
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## 15733 0 9.286074 12.80889 10.908379
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## 15737 0 9.688510 12.95809 11.205406
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## 15743 0 10.295404 13.21189 11.666179
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## 15789 0 13.432372 18.82567 15.889247
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## 15835 0 9.286074 12.80889 10.908379
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## 15839 0 9.688510 12.95809 11.205406
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## 15843 0 10.093741 13.13322 11.510520
## 15845 0 10.295404 13.21189 11.666179
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## 15889 0 13.353466 18.42843 15.677241
## 15891 0 13.432372 18.82567 15.889247
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## 15909 0 14.012368 22.99509 17.931080
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## 15983 0 13.029273 16.92409 14.857129
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## 15993 0 13.432372 18.82567 15.889247
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## 16011 0 14.012368 22.99509 17.931080
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## 16015 0 11.884939 14.34782 13.081450
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## 16019 0 7.442278 12.22654 9.537256
## 16021 0 7.616903 12.27506 9.666230
## 16023 0 7.794476 12.33184 9.796948
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## 16039 0 9.286074 12.80889 10.908379
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## 16045 0 9.898005 13.03710 11.356939
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## 16049 0 10.295404 13.21189 11.666179
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## 16063 0 11.639194 14.08734 12.816351
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## 16081 0 12.830995 16.26985 14.463305
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## 16085 0 13.029273 16.92409 14.857129
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## 16093 0 13.353466 18.42843 15.677241
## 16095 0 13.432372 18.82567 15.889247
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## 16113 0 14.012368 22.99509 17.931080
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## 16121 0 7.442278 12.22654 9.537256
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## 16141 0 9.286074 12.80889 10.908379
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## 16211 0 13.889533 22.00975 17.455773
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## 16215 0 14.012368 22.99509 17.931080
## 16217 0 14.071917 23.51784 18.173565
## 16219 0 11.884939 14.34782 13.081450
## 16221 0 7.278795 12.16782 9.410003
## 16223 0 7.442278 12.22654 9.537256
## 16225 0 7.616903 12.27506 9.666230
## 16227 0 7.794476 12.33184 9.796948
## 16229 0 7.968878 12.37636 9.929433
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## 16239 0 8.897316 12.69166 10.619226
## 16241 0 9.089560 12.74577 10.762832
## 16243 0 9.286074 12.80889 10.908379
## 16245 0 9.482701 12.88412 11.055895
## 16247 0 9.688510 12.95809 11.205406
## 16249 0 9.898005 13.03710 11.356939
## 16251 0 10.093741 13.13322 11.510520
## 16253 0 10.295404 13.21189 11.666179
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## 16265 0 11.452446 13.92574 12.645346
## 16267 0 11.639194 14.08734 12.816351
## 16269 0 11.802069 14.25588 12.989669
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## 16317 0 14.012368 22.99509 17.931080
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## 16517 0 13.889533 22.00975 17.455773
## 16519 0 13.954464 22.51002 17.691830
## 16521 0 14.012368 22.99509 17.931080
## 16523 0 14.071917 23.51784 18.173565
## 16525 0 11.884939 14.34782 13.081450
## 16527 0 7.278795 12.16782 9.410003
## 16529 0 7.442278 12.22654 9.537256
## 16531 0 7.616903 12.27506 9.666230
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## 16535 0 7.968878 12.37636 9.929433
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## 16549 0 9.286074 12.80889 10.908379
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## 16595 0 13.029273 16.92409 14.857129
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## 16929 0 14.012368 22.99509 17.931080
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## 16939 0 7.616903 12.27506 9.666230
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## 17003 0 13.029273 16.92409 14.857129
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## 17011 0 13.353466 18.42843 15.677241
## 17013 0 13.432372 18.82567 15.889247
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## 17021 0 13.688893 20.55819 16.766331
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## 17027 0 13.889533 22.00975 17.455773
## 17029 0 13.954464 22.51002 17.691830
## 17031 0 14.012368 22.99509 17.931080
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## 17035 0 11.884939 14.34782 13.081450
## 17037 0 7.278795 12.16782 9.410003
## 17039 0 7.442278 12.22654 9.537256
## 17041 0 7.616903 12.27506 9.666230
## 17043 0 7.794476 12.33184 9.796948
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## 17055 0 8.897316 12.69166 10.619226
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## 17059 0 9.286074 12.80889 10.908379
## 17061 0 9.482701 12.88412 11.055895
## 17063 0 9.688510 12.95809 11.205406
## 17065 0 9.898005 13.03710 11.356939
## 17067 0 10.093741 13.13322 11.510520
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## 17073 0 10.688480 13.41519 11.983840
## 17075 0 10.884731 13.51431 12.145900
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## 17081 0 11.452446 13.92574 12.645346
## 17083 0 11.639194 14.08734 12.816351
## 17085 0 11.802069 14.25588 12.989669
## 17087 0 11.954662 14.44565 13.165331
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## 17093 0 12.384249 15.12745 13.706697
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## 17105 0 13.029273 16.92409 14.857129
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## 17113 0 13.353466 18.42843 15.677241
## 17115 0 13.432372 18.82567 15.889247
## 17117 0 13.513453 19.23936 16.104120
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## 17133 0 14.012368 22.99509 17.931080
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## 17137 0 11.884939 14.34782 13.081450
## 17139 0 7.278795 12.16782 9.410003
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## 17335 0 13.954464 22.51002 17.691830
## 17337 0 14.012368 22.99509 17.931080
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## 17347 0 7.616903 12.27506 9.666230
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## 17365 0 9.286074 12.80889 10.908379
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## 17411 0 13.029273 16.92409 14.857129
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## 17421 0 13.432372 18.82567 15.889247
## 17423 0 13.513453 19.23936 16.104120
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## 17429 0 13.688893 20.55819 16.766331
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## 17439 0 14.012368 22.99509 17.931080
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## 17443 0 11.884939 14.34782 13.081450
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## 17449 0 7.616903 12.27506 9.666230
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## 17523 0 13.432372 18.82567 15.889247
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## 17541 0 14.012368 22.99509 17.931080
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## 17745 0 14.012368 22.99509 17.931080
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## 17773 0 9.286074 12.80889 10.908379
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## 17829 0 13.432372 18.82567 15.889247
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## 17843 0 13.889533 22.00975 17.455773
## 17845 0 13.954464 22.51002 17.691830
## 17847 0 14.012368 22.99509 17.931080
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## 17851 0 11.884939 14.34782 13.081450
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## 17855 0 7.442278 12.22654 9.537256
## 17857 0 7.616903 12.27506 9.666230
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## 17873 0 9.089560 12.74577 10.762832
## 17875 0 9.286074 12.80889 10.908379
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## 17883 0 10.093741 13.13322 11.510520
## 17885 0 10.295404 13.21189 11.666179
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## 17889 0 10.688480 13.41519 11.983840
## 17891 0 10.884731 13.51431 12.145900
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## 17897 0 11.452446 13.92574 12.645346
## 17899 0 11.639194 14.08734 12.816351
## 17901 0 11.802069 14.25588 12.989669
## 17903 0 11.954662 14.44565 13.165331
## 17905 0 12.095975 14.67114 13.343368
## 17907 0 12.245470 14.88313 13.523812
## 17909 0 12.384249 15.12745 13.706697
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## 17913 0 12.617263 15.66209 14.079920
## 17915 0 12.729714 15.96001 14.270325
## 17917 0 12.830995 16.26985 14.463305
## 17919 0 12.933504 16.58753 14.658895
## 17921 0 13.029273 16.92409 14.857129
## 17923 0 13.106783 17.27215 15.058045
## 17925 0 13.188133 17.64512 15.261677
## 17927 0 13.263707 18.01622 15.468064
## 17929 0 13.353466 18.42843 15.677241
## 17931 0 13.432372 18.82567 15.889247
## 17933 0 13.513453 19.23936 16.104120
## 17935 0 13.582972 19.67060 16.321898
## 17937 0 13.633575 20.10565 16.542622
## 17939 0 13.688893 20.55819 16.766331
## 17941 0 13.756667 21.01867 16.993065
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## 17945 0 13.889533 22.00975 17.455773
## 17947 0 13.954464 22.51002 17.691830
## 17949 0 14.012368 22.99509 17.931080
## 17951 0 14.071917 23.51784 18.173565
## 17953 0 11.884939 14.34782 13.081450
## 17955 0 7.278795 12.16782 9.410003
## 17957 0 7.442278 12.22654 9.537256
## 17959 0 7.616903 12.27506 9.666230
## 17961 0 7.794476 12.33184 9.796948
## 17963 0 7.968878 12.37636 9.929433
## 17965 0 8.156875 12.43860 10.063711
## 17967 0 8.340492 12.49641 10.199804
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## 17971 0 8.708284 12.62582 10.477537
## 17973 0 8.897316 12.69166 10.619226
## 17975 0 9.089560 12.74577 10.762832
## 17977 0 9.286074 12.80889 10.908379
## 17979 0 9.482701 12.88412 11.055895
## 17981 0 9.688510 12.95809 11.205406
## 17983 0 9.898005 13.03710 11.356939
## 17985 0 10.093741 13.13322 11.510520
## 17987 0 10.295404 13.21189 11.666179
## 17989 0 10.487528 13.31396 11.823943
## 17991 0 10.688480 13.41519 11.983840
## 17993 0 10.884731 13.51431 12.145900
## 17995 0 11.084090 13.63597 12.310151
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## 17999 0 11.452446 13.92574 12.645346
## 18001 0 11.639194 14.08734 12.816351
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## 18005 0 11.954662 14.44565 13.165331
## 18007 0 12.095975 14.67114 13.343368
## 18009 0 12.245470 14.88313 13.523812
## 18011 0 12.384249 15.12745 13.706697
## 18013 0 12.510622 15.39267 13.892055
## 18015 0 12.617263 15.66209 14.079920
## 18017 0 12.729714 15.96001 14.270325
## 18019 0 12.830995 16.26985 14.463305
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## 18023 0 13.029273 16.92409 14.857129
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## 18027 0 13.188133 17.64512 15.261677
## 18029 0 13.263707 18.01622 15.468064
## 18031 0 13.353466 18.42843 15.677241
## 18033 0 13.432372 18.82567 15.889247
## 18035 0 13.513453 19.23936 16.104120
## 18037 0 13.582972 19.67060 16.321898
## 18039 0 13.633575 20.10565 16.542622
## 18041 0 13.688893 20.55819 16.766331
## 18043 0 13.756667 21.01867 16.993065
## 18045 0 13.814921 21.49962 17.222865
## 18047 0 13.889533 22.00975 17.455773
## 18049 0 13.954464 22.51002 17.691830
## 18051 0 14.012368 22.99509 17.931080
## 18053 0 14.071917 23.51784 18.173565
## 18055 0 11.884939 14.34782 13.081450
## 18057 0 7.278795 12.16782 9.410003
## 18059 0 7.442278 12.22654 9.537256
## 18061 0 7.616903 12.27506 9.666230
## 18063 0 7.794476 12.33184 9.796948
## 18065 0 7.968878 12.37636 9.929433
## 18067 0 8.156875 12.43860 10.063711
## 18069 0 8.340492 12.49641 10.199804
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## 18073 0 8.708284 12.62582 10.477537
## 18075 0 8.897316 12.69166 10.619226
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## 18079 0 9.286074 12.80889 10.908379
## 18081 0 9.482701 12.88412 11.055895
## 18083 0 9.688510 12.95809 11.205406
## 18085 0 9.898005 13.03710 11.356939
## 18087 0 10.093741 13.13322 11.510520
## 18089 0 10.295404 13.21189 11.666179
## 18091 0 10.487528 13.31396 11.823943
## 18093 0 10.688480 13.41519 11.983840
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## 18103 0 11.639194 14.08734 12.816351
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## 18107 0 11.954662 14.44565 13.165331
## 18109 0 12.095975 14.67114 13.343368
## 18111 0 12.245470 14.88313 13.523812
## 18113 0 12.384249 15.12745 13.706697
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## 18119 0 12.729714 15.96001 14.270325
## 18121 0 12.830995 16.26985 14.463305
## 18123 0 12.933504 16.58753 14.658895
## 18125 0 13.029273 16.92409 14.857129
## 18127 0 13.106783 17.27215 15.058045
## 18129 0 13.188133 17.64512 15.261677
## 18131 0 13.263707 18.01622 15.468064
## 18133 0 13.353466 18.42843 15.677241
## 18135 0 13.432372 18.82567 15.889247
## 18137 0 13.513453 19.23936 16.104120
## 18139 0 13.582972 19.67060 16.321898
## 18141 0 13.633575 20.10565 16.542622
## 18143 0 13.688893 20.55819 16.766331
## 18145 0 13.756667 21.01867 16.993065
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## 18149 0 13.889533 22.00975 17.455773
## 18151 0 13.954464 22.51002 17.691830
## 18153 0 14.012368 22.99509 17.931080
## 18155 0 14.071917 23.51784 18.173565
## 18157 0 11.884939 14.34782 13.081450
## 18159 0 7.278795 12.16782 9.410003
## 18161 0 7.442278 12.22654 9.537256
## 18163 0 7.616903 12.27506 9.666230
## 18165 0 7.794476 12.33184 9.796948
## 18167 0 7.968878 12.37636 9.929433
## 18169 0 8.156875 12.43860 10.063711
## 18171 0 8.340492 12.49641 10.199804
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## 18175 0 8.708284 12.62582 10.477537
## 18177 0 8.897316 12.69166 10.619226
## 18179 0 9.089560 12.74577 10.762832
## 18181 0 9.286074 12.80889 10.908379
## 18183 0 9.482701 12.88412 11.055895
## 18185 0 9.688510 12.95809 11.205406
## 18187 0 9.898005 13.03710 11.356939
## 18189 0 10.093741 13.13322 11.510520
## 18191 0 10.295404 13.21189 11.666179
## 18193 0 10.487528 13.31396 11.823943
## 18195 0 10.688480 13.41519 11.983840
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## 18203 0 11.452446 13.92574 12.645346
## 18205 0 11.639194 14.08734 12.816351
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## 18209 0 11.954662 14.44565 13.165331
## 18211 0 12.095975 14.67114 13.343368
## 18213 0 12.245470 14.88313 13.523812
## 18215 0 12.384249 15.12745 13.706697
## 18217 0 12.510622 15.39267 13.892055
## 18219 0 12.617263 15.66209 14.079920
## 18221 0 12.729714 15.96001 14.270325
## 18223 0 12.830995 16.26985 14.463305
## 18225 0 12.933504 16.58753 14.658895
## 18227 0 13.029273 16.92409 14.857129
## 18229 0 13.106783 17.27215 15.058045
## 18231 0 13.188133 17.64512 15.261677
## 18233 0 13.263707 18.01622 15.468064
## 18235 0 13.353466 18.42843 15.677241
## 18237 0 13.432372 18.82567 15.889247
## 18239 0 13.513453 19.23936 16.104120
## 18241 0 13.582972 19.67060 16.321898
## 18243 0 13.633575 20.10565 16.542622
## 18245 0 13.688893 20.55819 16.766331
## 18247 0 13.756667 21.01867 16.993065
## 18249 0 13.814921 21.49962 17.222865
## 18251 0 13.889533 22.00975 17.455773
## 18253 0 13.954464 22.51002 17.691830
## 18255 0 14.012368 22.99509 17.931080
## 18257 0 14.071917 23.51784 18.173565
## 18259 0 11.884939 14.34782 13.081450
## 18261 0 7.278795 12.16782 9.410003
## 18263 0 7.442278 12.22654 9.537256
## 18265 0 7.616903 12.27506 9.666230
## 18267 0 7.794476 12.33184 9.796948
## 18269 0 7.968878 12.37636 9.929433
## 18271 0 8.156875 12.43860 10.063711
## 18273 0 8.340492 12.49641 10.199804
## 18275 0 8.522020 12.56565 10.337738
## 18277 0 8.708284 12.62582 10.477537
## 18279 0 8.897316 12.69166 10.619226
## 18281 0 9.089560 12.74577 10.762832
## 18283 0 9.286074 12.80889 10.908379
## 18285 0 9.482701 12.88412 11.055895
## 18287 0 9.688510 12.95809 11.205406
## 18289 0 9.898005 13.03710 11.356939
## 18291 0 10.093741 13.13322 11.510520
## 18293 0 10.295404 13.21189 11.666179
## 18295 0 10.487528 13.31396 11.823943
## 18297 0 10.688480 13.41519 11.983840
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## 18301 0 11.084090 13.63597 12.310151
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## 18305 0 11.452446 13.92574 12.645346
## 18307 0 11.639194 14.08734 12.816351
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## 18311 0 11.954662 14.44565 13.165331
## 18313 0 12.095975 14.67114 13.343368
## 18315 0 12.245470 14.88313 13.523812
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## 18323 0 12.729714 15.96001 14.270325
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## 18329 0 13.029273 16.92409 14.857129
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## 18333 0 13.188133 17.64512 15.261677
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## 18339 0 13.432372 18.82567 15.889247
## 18341 0 13.513453 19.23936 16.104120
## 18343 0 13.582972 19.67060 16.321898
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## 18357 0 14.012368 22.99509 17.931080
## 18359 0 14.071917 23.51784 18.173565
## 18361 0 11.884939 14.34782 13.081450
## 18363 0 7.278795 12.16782 9.410003
## 18365 0 7.442278 12.22654 9.537256
## 18367 0 7.616903 12.27506 9.666230
## 18369 0 7.794476 12.33184 9.796948
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## 18379 0 8.708284 12.62582 10.477537
## 18381 0 8.897316 12.69166 10.619226
## 18383 0 9.089560 12.74577 10.762832
## 18385 0 9.286074 12.80889 10.908379
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## 18391 0 9.898005 13.03710 11.356939
## 18393 0 10.093741 13.13322 11.510520
## 18395 0 10.295404 13.21189 11.666179
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## 18409 0 11.639194 14.08734 12.816351
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## 18423 0 12.617263 15.66209 14.079920
## 18425 0 12.729714 15.96001 14.270325
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## 18429 0 12.933504 16.58753 14.658895
## 18431 0 13.029273 16.92409 14.857129
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## 18439 0 13.353466 18.42843 15.677241
## 18441 0 13.432372 18.82567 15.889247
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## 18445 0 13.582972 19.67060 16.321898
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## 18449 0 13.688893 20.55819 16.766331
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## 18453 0 13.814921 21.49962 17.222865
## 18455 0 13.889533 22.00975 17.455773
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## 18459 0 14.012368 22.99509 17.931080
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## 18463 0 11.884939 14.34782 13.081450
## 18465 0 7.278795 12.16782 9.410003
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## 18469 0 7.616903 12.27506 9.666230
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## 18481 0 8.708284 12.62582 10.477537
## 18483 0 8.897316 12.69166 10.619226
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## 18487 0 9.286074 12.80889 10.908379
## 18489 0 9.482701 12.88412 11.055895
## 18491 0 9.688510 12.95809 11.205406
## 18493 0 9.898005 13.03710 11.356939
## 18495 0 10.093741 13.13322 11.510520
## 18497 0 10.295404 13.21189 11.666179
## 18499 0 10.487528 13.31396 11.823943
## 18501 0 10.688480 13.41519 11.983840
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## 18505 0 11.084090 13.63597 12.310151
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## 18511 0 11.639194 14.08734 12.816351
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## 18519 0 12.245470 14.88313 13.523812
## 18521 0 12.384249 15.12745 13.706697
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## 18525 0 12.617263 15.66209 14.079920
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## 18529 0 12.830995 16.26985 14.463305
## 18531 0 12.933504 16.58753 14.658895
## 18533 0 13.029273 16.92409 14.857129
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## 18537 0 13.188133 17.64512 15.261677
## 18539 0 13.263707 18.01622 15.468064
## 18541 0 13.353466 18.42843 15.677241
## 18543 0 13.432372 18.82567 15.889247
## 18545 0 13.513453 19.23936 16.104120
## 18547 0 13.582972 19.67060 16.321898
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## 18557 0 13.889533 22.00975 17.455773
## 18559 0 13.954464 22.51002 17.691830
## 18561 0 14.012368 22.99509 17.931080
## 18563 0 14.071917 23.51784 18.173565
## 18565 0 11.884939 14.34782 13.081450
## 18567 0 7.278795 12.16782 9.410003
## 18569 0 7.442278 12.22654 9.537256
## 18571 0 7.616903 12.27506 9.666230
## 18573 0 7.794476 12.33184 9.796948
## 18575 0 7.968878 12.37636 9.929433
## 18577 0 8.156875 12.43860 10.063711
## 18579 0 8.340492 12.49641 10.199804
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## 18583 0 8.708284 12.62582 10.477537
## 18585 0 8.897316 12.69166 10.619226
## 18587 0 9.089560 12.74577 10.762832
## 18589 0 9.286074 12.80889 10.908379
## 18591 0 9.482701 12.88412 11.055895
## 18593 0 9.688510 12.95809 11.205406
## 18595 0 9.898005 13.03710 11.356939
## 18597 0 10.093741 13.13322 11.510520
## 18599 0 10.295404 13.21189 11.666179
## 18601 0 10.487528 13.31396 11.823943
## 18603 0 10.688480 13.41519 11.983840
## 18605 0 10.884731 13.51431 12.145900
## 18607 0 11.084090 13.63597 12.310151
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## 18611 0 11.452446 13.92574 12.645346
## 18613 0 11.639194 14.08734 12.816351
## 18615 0 11.802069 14.25588 12.989669
## 18617 0 11.954662 14.44565 13.165331
## 18619 0 12.095975 14.67114 13.343368
## 18621 0 12.245470 14.88313 13.523812
## 18623 0 12.384249 15.12745 13.706697
## 18625 0 12.510622 15.39267 13.892055
## 18627 0 12.617263 15.66209 14.079920
## 18629 0 12.729714 15.96001 14.270325
## 18631 0 12.830995 16.26985 14.463305
## 18633 0 12.933504 16.58753 14.658895
## 18635 0 13.029273 16.92409 14.857129
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## 18639 0 13.188133 17.64512 15.261677
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## 18643 0 13.353466 18.42843 15.677241
## 18645 0 13.432372 18.82567 15.889247
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## 18649 0 13.582972 19.67060 16.321898
## 18651 0 13.633575 20.10565 16.542622
## 18653 0 13.688893 20.55819 16.766331
## 18655 0 13.756667 21.01867 16.993065
## 18657 0 13.814921 21.49962 17.222865
## 18659 0 13.889533 22.00975 17.455773
## 18661 0 13.954464 22.51002 17.691830
## 18663 0 14.012368 22.99509 17.931080
## 18665 0 14.071917 23.51784 18.173565
## 18667 0 11.884939 14.34782 13.081450
## 18669 0 7.278795 12.16782 9.410003
## 18671 0 7.442278 12.22654 9.537256
## 18673 0 7.616903 12.27506 9.666230
## 18675 0 7.794476 12.33184 9.796948
## 18677 0 7.968878 12.37636 9.929433
## 18679 0 8.156875 12.43860 10.063711
## 18681 0 8.340492 12.49641 10.199804
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## 18685 0 8.708284 12.62582 10.477537
## 18687 0 8.897316 12.69166 10.619226
## 18689 0 9.089560 12.74577 10.762832
## 18691 0 9.286074 12.80889 10.908379
## 18693 0 9.482701 12.88412 11.055895
## 18695 0 9.688510 12.95809 11.205406
## 18697 0 9.898005 13.03710 11.356939
## 18699 0 10.093741 13.13322 11.510520
## 18701 0 10.295404 13.21189 11.666179
## 18703 0 10.487528 13.31396 11.823943
## 18705 0 10.688480 13.41519 11.983840
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## 18713 0 11.452446 13.92574 12.645346
## 18715 0 11.639194 14.08734 12.816351
## 18717 0 11.802069 14.25588 12.989669
## 18719 0 11.954662 14.44565 13.165331
## 18721 0 12.095975 14.67114 13.343368
## 18723 0 12.245470 14.88313 13.523812
## 18725 0 12.384249 15.12745 13.706697
## 18727 0 12.510622 15.39267 13.892055
## 18729 0 12.617263 15.66209 14.079920
## 18731 0 12.729714 15.96001 14.270325
## 18733 0 12.830995 16.26985 14.463305
## 18735 0 12.933504 16.58753 14.658895
## 18737 0 13.029273 16.92409 14.857129
## 18739 0 13.106783 17.27215 15.058045
## 18741 0 13.188133 17.64512 15.261677
## 18743 0 13.263707 18.01622 15.468064
## 18745 0 13.353466 18.42843 15.677241
## 18747 0 13.432372 18.82567 15.889247
## 18749 0 13.513453 19.23936 16.104120
## 18751 0 13.582972 19.67060 16.321898
## 18753 0 13.633575 20.10565 16.542622
## 18755 0 13.688893 20.55819 16.766331
## 18757 0 13.756667 21.01867 16.993065
## 18759 0 13.814921 21.49962 17.222865
## 18761 0 13.889533 22.00975 17.455773
## 18763 0 13.954464 22.51002 17.691830
## 18765 0 14.012368 22.99509 17.931080
## 18767 0 14.071917 23.51784 18.173565
## 18769 0 11.884939 14.34782 13.081450
## 18771 0 7.278795 12.16782 9.410003
## 18773 0 7.442278 12.22654 9.537256
## 18775 0 7.616903 12.27506 9.666230
## 18777 0 7.794476 12.33184 9.796948
## 18779 0 7.968878 12.37636 9.929433
## 18781 0 8.156875 12.43860 10.063711
## 18783 0 8.340492 12.49641 10.199804
## 18785 0 8.522020 12.56565 10.337738
## 18787 0 8.708284 12.62582 10.477537
## 18789 0 8.897316 12.69166 10.619226
## 18791 0 9.089560 12.74577 10.762832
## 18793 0 9.286074 12.80889 10.908379
## 18795 0 9.482701 12.88412 11.055895
## 18797 0 9.688510 12.95809 11.205406
## 18799 0 9.898005 13.03710 11.356939
## 18801 0 10.093741 13.13322 11.510520
## 18803 0 10.295404 13.21189 11.666179
## 18805 0 10.487528 13.31396 11.823943
## 18807 0 10.688480 13.41519 11.983840
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## 18811 0 11.084090 13.63597 12.310151
## 18813 0 11.273297 13.76852 12.476623
## 18815 0 11.452446 13.92574 12.645346
## 18817 0 11.639194 14.08734 12.816351
## 18819 0 11.802069 14.25588 12.989669
## 18821 0 11.954662 14.44565 13.165331
## 18823 0 12.095975 14.67114 13.343368
## 18825 0 12.245470 14.88313 13.523812
## 18827 0 12.384249 15.12745 13.706697
## 18829 0 12.510622 15.39267 13.892055
## 18831 0 12.617263 15.66209 14.079920
## 18833 0 12.729714 15.96001 14.270325
## 18835 0 12.830995 16.26985 14.463305
## 18837 0 12.933504 16.58753 14.658895
## 18839 0 13.029273 16.92409 14.857129
## 18841 0 13.106783 17.27215 15.058045
## 18843 0 13.188133 17.64512 15.261677
## 18845 0 13.263707 18.01622 15.468064
## 18847 0 13.353466 18.42843 15.677241
## 18849 0 13.432372 18.82567 15.889247
## 18851 0 13.513453 19.23936 16.104120
## 18853 0 13.582972 19.67060 16.321898
## 18855 0 13.633575 20.10565 16.542622
## 18857 0 13.688893 20.55819 16.766331
## 18859 0 13.756667 21.01867 16.993065
## 18861 0 13.814921 21.49962 17.222865
## 18863 0 13.889533 22.00975 17.455773
## 18865 0 13.954464 22.51002 17.691830
## 18867 0 14.012368 22.99509 17.931080
## 18869 0 14.071917 23.51784 18.173565
## 18871 0 11.884939 14.34782 13.081450
## 18873 0 7.278795 12.16782 9.410003
## 18875 0 7.442278 12.22654 9.537256
## 18877 0 7.616903 12.27506 9.666230
## 18879 0 7.794476 12.33184 9.796948
## 18881 0 7.968878 12.37636 9.929433
## 18883 0 8.156875 12.43860 10.063711
## 18885 0 8.340492 12.49641 10.199804
## 18887 0 8.522020 12.56565 10.337738
## 18889 0 8.708284 12.62582 10.477537
## 18891 0 8.897316 12.69166 10.619226
## 18893 0 9.089560 12.74577 10.762832
## 18895 0 9.286074 12.80889 10.908379
## 18897 0 9.482701 12.88412 11.055895
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## 18903 0 10.093741 13.13322 11.510520
## 18905 0 10.295404 13.21189 11.666179
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## 18909 0 10.688480 13.41519 11.983840
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## 18919 0 11.639194 14.08734 12.816351
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## 18929 0 12.384249 15.12745 13.706697
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## 18933 0 12.617263 15.66209 14.079920
## 18935 0 12.729714 15.96001 14.270325
## 18937 0 12.830995 16.26985 14.463305
## 18939 0 12.933504 16.58753 14.658895
## 18941 0 13.029273 16.92409 14.857129
## 18943 0 13.106783 17.27215 15.058045
## 18945 0 13.188133 17.64512 15.261677
## 18947 0 13.263707 18.01622 15.468064
## 18949 0 13.353466 18.42843 15.677241
## 18951 0 13.432372 18.82567 15.889247
## 18953 0 13.513453 19.23936 16.104120
## 18955 0 13.582972 19.67060 16.321898
## 18957 0 13.633575 20.10565 16.542622
## 18959 0 13.688893 20.55819 16.766331
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## 18963 0 13.814921 21.49962 17.222865
## 18965 0 13.889533 22.00975 17.455773
## 18967 0 13.954464 22.51002 17.691830
## 18969 0 14.012368 22.99509 17.931080
## 18971 0 14.071917 23.51784 18.173565
## 18973 0 11.884939 14.34782 13.081450
## 18975 0 7.278795 12.16782 9.410003
## 18977 0 7.442278 12.22654 9.537256
## 18979 0 7.616903 12.27506 9.666230
## 18981 0 7.794476 12.33184 9.796948
## 18983 0 7.968878 12.37636 9.929433
## 18985 0 8.156875 12.43860 10.063711
## 18987 0 8.340492 12.49641 10.199804
## 18989 0 8.522020 12.56565 10.337738
## 18991 0 8.708284 12.62582 10.477537
## 18993 0 8.897316 12.69166 10.619226
## 18995 0 9.089560 12.74577 10.762832
## 18997 0 9.286074 12.80889 10.908379
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## 19001 0 9.688510 12.95809 11.205406
## 19003 0 9.898005 13.03710 11.356939
## 19005 0 10.093741 13.13322 11.510520
## 19007 0 10.295404 13.21189 11.666179
## 19009 0 10.487528 13.31396 11.823943
## 19011 0 10.688480 13.41519 11.983840
## 19013 0 10.884731 13.51431 12.145900
## 19015 0 11.084090 13.63597 12.310151
## 19017 0 11.273297 13.76852 12.476623
## 19019 0 11.452446 13.92574 12.645346
## 19021 0 11.639194 14.08734 12.816351
## 19023 0 11.802069 14.25588 12.989669
## 19025 0 11.954662 14.44565 13.165331
## 19027 0 12.095975 14.67114 13.343368
## 19029 0 12.245470 14.88313 13.523812
## 19031 0 12.384249 15.12745 13.706697
## 19033 0 12.510622 15.39267 13.892055
## 19035 0 12.617263 15.66209 14.079920
## 19037 0 12.729714 15.96001 14.270325
## 19039 0 12.830995 16.26985 14.463305
## 19041 0 12.933504 16.58753 14.658895
## 19043 0 13.029273 16.92409 14.857129
## 19045 0 13.106783 17.27215 15.058045
## 19047 0 13.188133 17.64512 15.261677
## 19049 0 13.263707 18.01622 15.468064
## 19051 0 13.353466 18.42843 15.677241
## 19053 0 13.432372 18.82567 15.889247
## 19055 0 13.513453 19.23936 16.104120
## 19057 0 13.582972 19.67060 16.321898
## 19059 0 13.633575 20.10565 16.542622
## 19061 0 13.688893 20.55819 16.766331
## 19063 0 13.756667 21.01867 16.993065
## 19065 0 13.814921 21.49962 17.222865
## 19067 0 13.889533 22.00975 17.455773
## 19069 0 13.954464 22.51002 17.691830
## 19071 0 14.012368 22.99509 17.931080
## 19073 0 14.071917 23.51784 18.173565
## 19075 0 11.884939 14.34782 13.081450
## 19077 0 7.278795 12.16782 9.410003
## 19079 0 7.442278 12.22654 9.537256
## 19081 0 7.616903 12.27506 9.666230
## 19083 0 7.794476 12.33184 9.796948
## 19085 0 7.968878 12.37636 9.929433
## 19087 0 8.156875 12.43860 10.063711
## 19089 0 8.340492 12.49641 10.199804
## 19091 0 8.522020 12.56565 10.337738
## 19093 0 8.708284 12.62582 10.477537
## 19095 0 8.897316 12.69166 10.619226
## 19097 0 9.089560 12.74577 10.762832
## 19099 0 9.286074 12.80889 10.908379
## 19101 0 9.482701 12.88412 11.055895
## 19103 0 9.688510 12.95809 11.205406
## 19105 0 9.898005 13.03710 11.356939
## 19107 0 10.093741 13.13322 11.510520
## 19109 0 10.295404 13.21189 11.666179
## 19111 0 10.487528 13.31396 11.823943
## 19113 0 10.688480 13.41519 11.983840
## 19115 0 10.884731 13.51431 12.145900
## 19117 0 11.084090 13.63597 12.310151
## 19119 0 11.273297 13.76852 12.476623
## 19121 0 11.452446 13.92574 12.645346
## 19123 0 11.639194 14.08734 12.816351
## 19125 0 11.802069 14.25588 12.989669
## 19127 0 11.954662 14.44565 13.165331
## 19129 0 12.095975 14.67114 13.343368
## 19131 0 12.245470 14.88313 13.523812
## 19133 0 12.384249 15.12745 13.706697
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## 19137 0 12.617263 15.66209 14.079920
## 19139 0 12.729714 15.96001 14.270325
## 19141 0 12.830995 16.26985 14.463305
## 19143 0 12.933504 16.58753 14.658895
## 19145 0 13.029273 16.92409 14.857129
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## 19149 0 13.188133 17.64512 15.261677
## 19151 0 13.263707 18.01622 15.468064
## 19153 0 13.353466 18.42843 15.677241
## 19155 0 13.432372 18.82567 15.889247
## 19157 0 13.513453 19.23936 16.104120
## 19159 0 13.582972 19.67060 16.321898
## 19161 0 13.633575 20.10565 16.542622
## 19163 0 13.688893 20.55819 16.766331
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## 19167 0 13.814921 21.49962 17.222865
## 19169 0 13.889533 22.00975 17.455773
## 19171 0 13.954464 22.51002 17.691830
## 19173 0 14.012368 22.99509 17.931080
## 19175 0 14.071917 23.51784 18.173565
## 19177 0 11.884939 14.34782 13.081450
## 19179 0 7.278795 12.16782 9.410003
## 19181 0 7.442278 12.22654 9.537256
## 19183 0 7.616903 12.27506 9.666230
## 19185 0 7.794476 12.33184 9.796948
## 19187 0 7.968878 12.37636 9.929433
## 19189 0 8.156875 12.43860 10.063711
## 19191 0 8.340492 12.49641 10.199804
## 19193 0 8.522020 12.56565 10.337738
## 19195 0 8.708284 12.62582 10.477537
## 19197 0 8.897316 12.69166 10.619226
## 19199 0 9.089560 12.74577 10.762832
## 19201 0 9.286074 12.80889 10.908379
## 19203 0 9.482701 12.88412 11.055895
## 19205 0 9.688510 12.95809 11.205406
## 19207 0 9.898005 13.03710 11.356939
## 19209 0 10.093741 13.13322 11.510520
## 19211 0 10.295404 13.21189 11.666179
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## 19215 0 10.688480 13.41519 11.983840
## 19217 0 10.884731 13.51431 12.145900
## 19219 0 11.084090 13.63597 12.310151
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## 19223 0 11.452446 13.92574 12.645346
## 19225 0 11.639194 14.08734 12.816351
## 19227 0 11.802069 14.25588 12.989669
## 19229 0 11.954662 14.44565 13.165331
## 19231 0 12.095975 14.67114 13.343368
## 19233 0 12.245470 14.88313 13.523812
## 19235 0 12.384249 15.12745 13.706697
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## 19239 0 12.617263 15.66209 14.079920
## 19241 0 12.729714 15.96001 14.270325
## 19243 0 12.830995 16.26985 14.463305
## 19245 0 12.933504 16.58753 14.658895
## 19247 0 13.029273 16.92409 14.857129
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## 19251 0 13.188133 17.64512 15.261677
## 19253 0 13.263707 18.01622 15.468064
## 19255 0 13.353466 18.42843 15.677241
## 19257 0 13.432372 18.82567 15.889247
## 19259 0 13.513453 19.23936 16.104120
## 19261 0 13.582972 19.67060 16.321898
## 19263 0 13.633575 20.10565 16.542622
## 19265 0 13.688893 20.55819 16.766331
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## 19275 0 14.012368 22.99509 17.931080
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## 19283 0 7.442278 12.22654 9.537256
## 19285 0 7.616903 12.27506 9.666230
## 19287 0 7.794476 12.33184 9.796948
## 19289 0 7.968878 12.37636 9.929433
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## 19293 0 8.340492 12.49641 10.199804
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## 19297 0 8.708284 12.62582 10.477537
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## 19303 0 9.286074 12.80889 10.908379
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## 19307 0 9.688510 12.95809 11.205406
## 19309 0 9.898005 13.03710 11.356939
## 19311 0 10.093741 13.13322 11.510520
## 19313 0 10.295404 13.21189 11.666179
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## 19331 0 11.954662 14.44565 13.165331
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## 19335 0 12.245470 14.88313 13.523812
## 19337 0 12.384249 15.12745 13.706697
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## 19345 0 12.830995 16.26985 14.463305
## 19347 0 12.933504 16.58753 14.658895
## 19349 0 13.029273 16.92409 14.857129
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## 19373 0 13.889533 22.00975 17.455773
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## 19377 0 14.012368 22.99509 17.931080
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## 19381 0 11.884939 14.34782 13.081450
## 19383 0 7.278795 12.16782 9.410003
## 19385 0 7.442278 12.22654 9.537256
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## 19391 0 7.968878 12.37636 9.929433
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## 19395 0 8.340492 12.49641 10.199804
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## 19399 0 8.708284 12.62582 10.477537
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## 19405 0 9.286074 12.80889 10.908379
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## 19409 0 9.688510 12.95809 11.205406
## 19411 0 9.898005 13.03710 11.356939
## 19413 0 10.093741 13.13322 11.510520
## 19415 0 10.295404 13.21189 11.666179
## 19417 0 10.487528 13.31396 11.823943
## 19419 0 10.688480 13.41519 11.983840
## 19421 0 10.884731 13.51431 12.145900
## 19423 0 11.084090 13.63597 12.310151
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## 19427 0 11.452446 13.92574 12.645346
## 19429 0 11.639194 14.08734 12.816351
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## 19433 0 11.954662 14.44565 13.165331
## 19435 0 12.095975 14.67114 13.343368
## 19437 0 12.245470 14.88313 13.523812
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## 19443 0 12.617263 15.66209 14.079920
## 19445 0 12.729714 15.96001 14.270325
## 19447 0 12.830995 16.26985 14.463305
## 19449 0 12.933504 16.58753 14.658895
## 19451 0 13.029273 16.92409 14.857129
## 19453 0 13.106783 17.27215 15.058045
## 19455 0 13.188133 17.64512 15.261677
## 19457 0 13.263707 18.01622 15.468064
## 19459 0 13.353466 18.42843 15.677241
## 19461 0 13.432372 18.82567 15.889247
## 19463 0 13.513453 19.23936 16.104120
## 19465 0 13.582972 19.67060 16.321898
## 19467 0 13.633575 20.10565 16.542622
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## 19471 0 13.756667 21.01867 16.993065
## 19473 0 13.814921 21.49962 17.222865
## 19475 0 13.889533 22.00975 17.455773
## 19477 0 13.954464 22.51002 17.691830
## 19479 0 14.012368 22.99509 17.931080
## 19481 0 14.071917 23.51784 18.173565
## 19483 0 11.884939 14.34782 13.081450
## 19485 0 7.278795 12.16782 9.410003
## 19487 0 7.442278 12.22654 9.537256
## 19489 0 7.616903 12.27506 9.666230
## 19491 0 7.794476 12.33184 9.796948
## 19493 0 7.968878 12.37636 9.929433
## 19495 0 8.156875 12.43860 10.063711
## 19497 0 8.340492 12.49641 10.199804
## 19499 0 8.522020 12.56565 10.337738
## 19501 0 8.708284 12.62582 10.477537
## 19503 0 8.897316 12.69166 10.619226
## 19505 0 9.089560 12.74577 10.762832
## 19507 0 9.286074 12.80889 10.908379
## 19509 0 9.482701 12.88412 11.055895
## 19511 0 9.688510 12.95809 11.205406
## 19513 0 9.898005 13.03710 11.356939
## 19515 0 10.093741 13.13322 11.510520
## 19517 0 10.295404 13.21189 11.666179
## 19519 0 10.487528 13.31396 11.823943
## 19521 0 10.688480 13.41519 11.983840
## 19523 0 10.884731 13.51431 12.145900
## 19525 0 11.084090 13.63597 12.310151
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## 19529 0 11.452446 13.92574 12.645346
## 19531 0 11.639194 14.08734 12.816351
## 19533 0 11.802069 14.25588 12.989669
## 19535 0 11.954662 14.44565 13.165331
## 19537 0 12.095975 14.67114 13.343368
## 19539 0 12.245470 14.88313 13.523812
## 19541 0 12.384249 15.12745 13.706697
## 19543 0 12.510622 15.39267 13.892055
## 19545 0 12.617263 15.66209 14.079920
## 19547 0 12.729714 15.96001 14.270325
## 19549 0 12.830995 16.26985 14.463305
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## 19553 0 13.029273 16.92409 14.857129
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## 19557 0 13.188133 17.64512 15.261677
## 19559 0 13.263707 18.01622 15.468064
## 19561 0 13.353466 18.42843 15.677241
## 19563 0 13.432372 18.82567 15.889247
## 19565 0 13.513453 19.23936 16.104120
## 19567 0 13.582972 19.67060 16.321898
## 19569 0 13.633575 20.10565 16.542622
## 19571 0 13.688893 20.55819 16.766331
## 19573 0 13.756667 21.01867 16.993065
## 19575 0 13.814921 21.49962 17.222865
## 19577 0 13.889533 22.00975 17.455773
## 19579 0 13.954464 22.51002 17.691830
## 19581 0 14.012368 22.99509 17.931080
## 19583 0 14.071917 23.51784 18.173565
## 19585 0 11.884939 14.34782 13.081450
## 19587 0 7.278795 12.16782 9.410003
## 19589 0 7.442278 12.22654 9.537256
## 19591 0 7.616903 12.27506 9.666230
## 19593 0 7.794476 12.33184 9.796948
## 19595 0 7.968878 12.37636 9.929433
## 19597 0 8.156875 12.43860 10.063711
## 19599 0 8.340492 12.49641 10.199804
## 19601 0 8.522020 12.56565 10.337738
## 19603 0 8.708284 12.62582 10.477537
## 19605 0 8.897316 12.69166 10.619226
## 19607 0 9.089560 12.74577 10.762832
## 19609 0 9.286074 12.80889 10.908379
## 19611 0 9.482701 12.88412 11.055895
## 19613 0 9.688510 12.95809 11.205406
## 19615 0 9.898005 13.03710 11.356939
## 19617 0 10.093741 13.13322 11.510520
## 19619 0 10.295404 13.21189 11.666179
## 19621 0 10.487528 13.31396 11.823943
## 19623 0 10.688480 13.41519 11.983840
## 19625 0 10.884731 13.51431 12.145900
## 19627 0 11.084090 13.63597 12.310151
## 19629 0 11.273297 13.76852 12.476623
## 19631 0 11.452446 13.92574 12.645346
## 19633 0 11.639194 14.08734 12.816351
## 19635 0 11.802069 14.25588 12.989669
## 19637 0 11.954662 14.44565 13.165331
## 19639 0 12.095975 14.67114 13.343368
## 19641 0 12.245470 14.88313 13.523812
## 19643 0 12.384249 15.12745 13.706697
## 19645 0 12.510622 15.39267 13.892055
## 19647 0 12.617263 15.66209 14.079920
## 19649 0 12.729714 15.96001 14.270325
## 19651 0 12.830995 16.26985 14.463305
## 19653 0 12.933504 16.58753 14.658895
## 19655 0 13.029273 16.92409 14.857129
## 19657 0 13.106783 17.27215 15.058045
## 19659 0 13.188133 17.64512 15.261677
## 19661 0 13.263707 18.01622 15.468064
## 19663 0 13.353466 18.42843 15.677241
## 19665 0 13.432372 18.82567 15.889247
## 19667 0 13.513453 19.23936 16.104120
## 19669 0 13.582972 19.67060 16.321898
## 19671 0 13.633575 20.10565 16.542622
## 19673 0 13.688893 20.55819 16.766331
## 19675 0 13.756667 21.01867 16.993065
## 19677 0 13.814921 21.49962 17.222865
## 19679 0 13.889533 22.00975 17.455773
## 19681 0 13.954464 22.51002 17.691830
## 19683 0 14.012368 22.99509 17.931080
## 19685 0 14.071917 23.51784 18.173565
## 19687 0 11.884939 14.34782 13.081450
## 19689 0 7.278795 12.16782 9.410003
## 19691 0 7.442278 12.22654 9.537256
## 19693 0 7.616903 12.27506 9.666230
## 19695 0 7.794476 12.33184 9.796948
## 19697 0 7.968878 12.37636 9.929433
## 19699 0 8.156875 12.43860 10.063711
## 19701 0 8.340492 12.49641 10.199804
## 19703 0 8.522020 12.56565 10.337738
## 19705 0 8.708284 12.62582 10.477537
## 19707 0 8.897316 12.69166 10.619226
## 19709 0 9.089560 12.74577 10.762832
## 19711 0 9.286074 12.80889 10.908379
## 19713 0 9.482701 12.88412 11.055895
## 19715 0 9.688510 12.95809 11.205406
## 19717 0 9.898005 13.03710 11.356939
## 19719 0 10.093741 13.13322 11.510520
## 19721 0 10.295404 13.21189 11.666179
## 19723 0 10.487528 13.31396 11.823943
## 19725 0 10.688480 13.41519 11.983840
## 19727 0 10.884731 13.51431 12.145900
## 19729 0 11.084090 13.63597 12.310151
## 19731 0 11.273297 13.76852 12.476623
## 19733 0 11.452446 13.92574 12.645346
## 19735 0 11.639194 14.08734 12.816351
## 19737 0 11.802069 14.25588 12.989669
## 19739 0 11.954662 14.44565 13.165331
## 19741 0 12.095975 14.67114 13.343368
## 19743 0 12.245470 14.88313 13.523812
## 19745 0 12.384249 15.12745 13.706697
## 19747 0 12.510622 15.39267 13.892055
## 19749 0 12.617263 15.66209 14.079920
## 19751 0 12.729714 15.96001 14.270325
## 19753 0 12.830995 16.26985 14.463305
## 19755 0 12.933504 16.58753 14.658895
## 19757 0 13.029273 16.92409 14.857129
## 19759 0 13.106783 17.27215 15.058045
## 19761 0 13.188133 17.64512 15.261677
## 19763 0 13.263707 18.01622 15.468064
## 19765 0 13.353466 18.42843 15.677241
## 19767 0 13.432372 18.82567 15.889247
## 19769 0 13.513453 19.23936 16.104120
## 19771 0 13.582972 19.67060 16.321898
## 19773 0 13.633575 20.10565 16.542622
## 19775 0 13.688893 20.55819 16.766331
## 19777 0 13.756667 21.01867 16.993065
## 19779 0 13.814921 21.49962 17.222865
## 19781 0 13.889533 22.00975 17.455773
## 19783 0 13.954464 22.51002 17.691830
## 19785 0 14.012368 22.99509 17.931080
## 19787 0 14.071917 23.51784 18.173565
## 19789 0 11.884939 14.34782 13.081450
## 19791 0 7.278795 12.16782 9.410003
## 19793 0 7.442278 12.22654 9.537256
## 19795 0 7.616903 12.27506 9.666230
## 19797 0 7.794476 12.33184 9.796948
## 19799 0 7.968878 12.37636 9.929433
## 19801 0 8.156875 12.43860 10.063711
## 19803 0 8.340492 12.49641 10.199804
## 19805 0 8.522020 12.56565 10.337738
## 19807 0 8.708284 12.62582 10.477537
## 19809 0 8.897316 12.69166 10.619226
## 19811 0 9.089560 12.74577 10.762832
## 19813 0 9.286074 12.80889 10.908379
## 19815 0 9.482701 12.88412 11.055895
## 19817 0 9.688510 12.95809 11.205406
## 19819 0 9.898005 13.03710 11.356939
## 19821 0 10.093741 13.13322 11.510520
## 19823 0 10.295404 13.21189 11.666179
## 19825 0 10.487528 13.31396 11.823943
## 19827 0 10.688480 13.41519 11.983840
## 19829 0 10.884731 13.51431 12.145900
## 19831 0 11.084090 13.63597 12.310151
## 19833 0 11.273297 13.76852 12.476623
## 19835 0 11.452446 13.92574 12.645346
## 19837 0 11.639194 14.08734 12.816351
## 19839 0 11.802069 14.25588 12.989669
## 19841 0 11.954662 14.44565 13.165331
## 19843 0 12.095975 14.67114 13.343368
## 19845 0 12.245470 14.88313 13.523812
## 19847 0 12.384249 15.12745 13.706697
## 19849 0 12.510622 15.39267 13.892055
## 19851 0 12.617263 15.66209 14.079920
## 19853 0 12.729714 15.96001 14.270325
## 19855 0 12.830995 16.26985 14.463305
## 19857 0 12.933504 16.58753 14.658895
## 19859 0 13.029273 16.92409 14.857129
## 19861 0 13.106783 17.27215 15.058045
## 19863 0 13.188133 17.64512 15.261677
## 19865 0 13.263707 18.01622 15.468064
## 19867 0 13.353466 18.42843 15.677241
## 19869 0 13.432372 18.82567 15.889247
## 19871 0 13.513453 19.23936 16.104120
## 19873 0 13.582972 19.67060 16.321898
## 19875 0 13.633575 20.10565 16.542622
## 19877 0 13.688893 20.55819 16.766331
## 19879 0 13.756667 21.01867 16.993065
## 19881 0 13.814921 21.49962 17.222865
## 19883 0 13.889533 22.00975 17.455773
## 19885 0 13.954464 22.51002 17.691830
## 19887 0 14.012368 22.99509 17.931080
## 19889 0 14.071917 23.51784 18.173565
## 19891 0 11.884939 14.34782 13.081450
## 19893 0 7.278795 12.16782 9.410003
## 19895 0 7.442278 12.22654 9.537256
## 19897 0 7.616903 12.27506 9.666230
## 19899 0 7.794476 12.33184 9.796948
## 19901 0 7.968878 12.37636 9.929433
## 19903 0 8.156875 12.43860 10.063711
## 19905 0 8.340492 12.49641 10.199804
## 19907 0 8.522020 12.56565 10.337738
## 19909 0 8.708284 12.62582 10.477537
## 19911 0 8.897316 12.69166 10.619226
## 19913 0 9.089560 12.74577 10.762832
## 19915 0 9.286074 12.80889 10.908379
## 19917 0 9.482701 12.88412 11.055895
## 19919 0 9.688510 12.95809 11.205406
## 19921 0 9.898005 13.03710 11.356939
## 19923 0 10.093741 13.13322 11.510520
## 19925 0 10.295404 13.21189 11.666179
## 19927 0 10.487528 13.31396 11.823943
## 19929 0 10.688480 13.41519 11.983840
## 19931 0 10.884731 13.51431 12.145900
## 19933 0 11.084090 13.63597 12.310151
## 19935 0 11.273297 13.76852 12.476623
## 19937 0 11.452446 13.92574 12.645346
## 19939 0 11.639194 14.08734 12.816351
## 19941 0 11.802069 14.25588 12.989669
## 19943 0 11.954662 14.44565 13.165331
## 19945 0 12.095975 14.67114 13.343368
## 19947 0 12.245470 14.88313 13.523812
## 19949 0 12.384249 15.12745 13.706697
## 19951 0 12.510622 15.39267 13.892055
## 19953 0 12.617263 15.66209 14.079920
## 19955 0 12.729714 15.96001 14.270325
## 19957 0 12.830995 16.26985 14.463305
## 19959 0 12.933504 16.58753 14.658895
## 19961 0 13.029273 16.92409 14.857129
## 19963 0 13.106783 17.27215 15.058045
## 19965 0 13.188133 17.64512 15.261677
## 19967 0 13.263707 18.01622 15.468064
## 19969 0 13.353466 18.42843 15.677241
## 19971 0 13.432372 18.82567 15.889247
## 19973 0 13.513453 19.23936 16.104120
## 19975 0 13.582972 19.67060 16.321898
## 19977 0 13.633575 20.10565 16.542622
## 19979 0 13.688893 20.55819 16.766331
## 19981 0 13.756667 21.01867 16.993065
## 19983 0 13.814921 21.49962 17.222865
## 19985 0 13.889533 22.00975 17.455773
## 19987 0 13.954464 22.51002 17.691830
## 19989 0 14.012368 22.99509 17.931080
## 19991 0 14.071917 23.51784 18.173565
## 19993 0 11.884939 14.34782 13.081450
## 19995 0 7.278795 12.16782 9.410003
## 19997 0 7.442278 12.22654 9.537256
## 19999 0 7.616903 12.27506 9.666230
## 20001 0 7.794476 12.33184 9.796948
## 20003 0 7.968878 12.37636 9.929433
## 20005 0 8.156875 12.43860 10.063711
## 20007 0 8.340492 12.49641 10.199804
## 20009 0 8.522020 12.56565 10.337738
## 20011 0 8.708284 12.62582 10.477537
## 20013 0 8.897316 12.69166 10.619226
## 20015 0 9.089560 12.74577 10.762832
## 20017 0 9.286074 12.80889 10.908379
## 20019 0 9.482701 12.88412 11.055895
## 20021 0 9.688510 12.95809 11.205406
## 20023 0 9.898005 13.03710 11.356939
## 20025 0 10.093741 13.13322 11.510520
## 20027 0 10.295404 13.21189 11.666179
## 20029 0 10.487528 13.31396 11.823943
## 20031 0 10.688480 13.41519 11.983840
## 20033 0 10.884731 13.51431 12.145900
## 20035 0 11.084090 13.63597 12.310151
## 20037 0 11.273297 13.76852 12.476623
## 20039 0 11.452446 13.92574 12.645346
## 20041 0 11.639194 14.08734 12.816351
## 20043 0 11.802069 14.25588 12.989669
## 20045 0 11.954662 14.44565 13.165331
## 20047 0 12.095975 14.67114 13.343368
## 20049 0 12.245470 14.88313 13.523812
## 20051 0 12.384249 15.12745 13.706697
## 20053 0 12.510622 15.39267 13.892055
## 20055 0 12.617263 15.66209 14.079920
## 20057 0 12.729714 15.96001 14.270325
## 20059 0 12.830995 16.26985 14.463305
## 20061 0 12.933504 16.58753 14.658895
## 20063 0 13.029273 16.92409 14.857129
## 20065 0 13.106783 17.27215 15.058045
## 20067 0 13.188133 17.64512 15.261677
## 20069 0 13.263707 18.01622 15.468064
## 20071 0 13.353466 18.42843 15.677241
## 20073 0 13.432372 18.82567 15.889247
## 20075 0 13.513453 19.23936 16.104120
## 20077 0 13.582972 19.67060 16.321898
## 20079 0 13.633575 20.10565 16.542622
## 20081 0 13.688893 20.55819 16.766331
## 20083 0 13.756667 21.01867 16.993065
## 20085 0 13.814921 21.49962 17.222865
## 20087 0 13.889533 22.00975 17.455773
## 20089 0 13.954464 22.51002 17.691830
## 20091 0 14.012368 22.99509 17.931080
## 20093 0 14.071917 23.51784 18.173565
## 20095 0 11.884939 14.34782 13.081450
## 20097 0 7.278795 12.16782 9.410003
## 20099 0 7.442278 12.22654 9.537256
## 20101 0 7.616903 12.27506 9.666230
## 20103 0 7.794476 12.33184 9.796948
## 20105 0 7.968878 12.37636 9.929433
## 20107 0 8.156875 12.43860 10.063711
## 20109 0 8.340492 12.49641 10.199804
## 20111 0 8.522020 12.56565 10.337738
## 20113 0 8.708284 12.62582 10.477537
## 20115 0 8.897316 12.69166 10.619226
## 20117 0 9.089560 12.74577 10.762832
## 20119 0 9.286074 12.80889 10.908379
## 20121 0 9.482701 12.88412 11.055895
## 20123 0 9.688510 12.95809 11.205406
## 20125 0 9.898005 13.03710 11.356939
## 20127 0 10.093741 13.13322 11.510520
## 20129 0 10.295404 13.21189 11.666179
## 20131 0 10.487528 13.31396 11.823943
## 20133 0 10.688480 13.41519 11.983840
## 20135 0 10.884731 13.51431 12.145900
## 20137 0 11.084090 13.63597 12.310151
## 20139 0 11.273297 13.76852 12.476623
## 20141 0 11.452446 13.92574 12.645346
## 20143 0 11.639194 14.08734 12.816351
## 20145 0 11.802069 14.25588 12.989669
## 20147 0 11.954662 14.44565 13.165331
## 20149 0 12.095975 14.67114 13.343368
## 20151 0 12.245470 14.88313 13.523812
## 20153 0 12.384249 15.12745 13.706697
## 20155 0 12.510622 15.39267 13.892055
## 20157 0 12.617263 15.66209 14.079920
## 20159 0 12.729714 15.96001 14.270325
## 20161 0 12.830995 16.26985 14.463305
## 20163 0 12.933504 16.58753 14.658895
## 20165 0 13.029273 16.92409 14.857129
## 20167 0 13.106783 17.27215 15.058045
## 20169 0 13.188133 17.64512 15.261677
## 20171 0 13.263707 18.01622 15.468064
## 20173 0 13.353466 18.42843 15.677241
## 20175 0 13.432372 18.82567 15.889247
## 20177 0 13.513453 19.23936 16.104120
## 20179 0 13.582972 19.67060 16.321898
## 20181 0 13.633575 20.10565 16.542622
## 20183 0 13.688893 20.55819 16.766331
## 20185 0 13.756667 21.01867 16.993065
## 20187 0 13.814921 21.49962 17.222865
## 20189 0 13.889533 22.00975 17.455773
## 20191 0 13.954464 22.51002 17.691830
## 20193 0 14.012368 22.99509 17.931080
## 20195 0 14.071917 23.51784 18.173565
## 20197 0 11.884939 14.34782 13.081450
## 20199 0 7.278795 12.16782 9.410003
## 20201 0 7.442278 12.22654 9.537256
## [ reached getOption("max.print") -- omitted 201 rows ]### Plot amplitude lmer with trial number
pframe2$trt3 <- mapvalues(pframe2$trt2, from = c("Sham first", "Weighted first"),
to = c("Sham -> Weighted", "Weighted -> Sham"))
g0 <- ggplot(pframe2, aes(x=visitNum_centered, y=predMean))+
geom_line(aes(color = treatment))+
labs(y = expression ("Sonication acceleration "(m~s^{-2})), x = "Sonication number\n (0 is when treatment switched)") +
geom_ribbon(aes(x = visitNum_centered, ymin = blo, ymax = bhi, fill= treatment), alpha = 0.2) +
facet_wrap(~trt3) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
scale_fill_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = c(0.5, 0.89),
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0
ggsave(filename = file.path(figDir, "WeightedSham_Timeseries_amp.pdf"), width =5, height = 3.6)
g1 <- g0 + geom_point(data = newdf3[newdf3$visitNum_centered < 50,],
aes(x = visitNum_centered, y = amp_acc), position = position_jitter(width = 0.5), size = 0.1, pch = 16, alpha = 0.4) +
ylim(c(0, 165))
g1
ggsave(filename = file.path(figDir, "WeightedSham_Timeseries_withRawData.pdf"), width =5, height = 3.6)
g1 <- g0 + geom_point(data = newdf3[newdf3$visitNum_centered < 50,],
aes(x = visitNum_centered, y = amp_acc), position = position_jitter(width = 0.5), size = 0.1, pch = 16, alpha = 0.4) +
scale_y_log10(limits = c(2, 500)) +
annotation_logticks(sides = "l", color = 'grey', size = 0.2)
g1## Warning: Removed 50 rows containing missing values (geom_point).
ggsave(filename = file.path(figDir, "WeightedSham_Timeseries_withRawData_logScale.pdf"), width =5, height = 3.6)## Warning: Removed 50 rows containing missing values (geom_point).# make figure that isn't faceted by order of treatment
g03 <- ggplot(pframe2, aes(x=visitNum_centered, y=predMean))+
geom_line(aes(color = treatment))+
labs(y = expression ("Sonication acceleration "(m~s^{-2})), x = "Sonication number\n (0 is when treatment switched)") +
geom_ribbon(aes(x = visitNum_centered, ymin = blo, ymax = bhi, fill= treatment), alpha = 0.2) +
facet_wrap(~treatment) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
scale_fill_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = c(0.75, 0.8),
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="vertical")
g03
ggsave(filename = file.path(figDir, "WeightedSham_Timeseries_trtFacet.pdf"), width =5, height = 3.6)Show amplitude plot without visit number
look at visit number 1 (right at the time of switching)
# mean and 95% CI (without visit number)
g0_amp <- ggplot(pframe2[pframe2$visitNum_centered %in% c(1) & pframe2$IT == ITmean, ], aes(x=treatment, y=predMean))+
geom_point(aes(color = treatment), alpha = 1) +
labs(y = expression ("Sonication acceleration "(m~s^{-2})), x = "Flower treatment") +
geom_errorbar(aes(x = treatment, ymin = blo, ymax = bhi, color= treatment), alpha = 1, width = 0.1) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, option = "A", begin =0, end = 0) +
theme(legend.position = "none",
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0_amp
ggsave(filename = file.path(figDir, "WeightedSham_Amp_pointWhiskers_BW.pdf"), width =2.5, height = 3)
g0 <- ggplot(pframe2[pframe2$visitNum_centered %in% c(1) & pframe2$IT == ITmean, ], aes(x=treatment, y=predMean))+
geom_point(aes(color = treatment), alpha = 1) +
labs(y = expression ("Sonication acceleration "(m~s^{-2})), x = "Flower treatment") +
geom_errorbar(aes(x = treatment, ymin = blo, ymax = bhi, color= treatment), alpha = 1, width = 0.1) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = "none",
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0
ggsave(filename = file.path(figDir, "WeightedSham_Amp_pointWhiskers.pdf"), width =5, height = 3.6)
# fig 2b
g0IT <- ggplot(pframe2[pframe2$visitNum_centered %in% c(1), ], aes(x=IT, y=predMean))+
geom_line(aes(color = treatment), alpha = 1) +
labs(y = expression ("Sonication acceleration "(m~s^{-2})), x = "Intertegular span (mm)") +
geom_ribbon(aes(x = IT, ymin = blo, ymax = bhi, fill = treatment), alpha = 0.2) +
scale_color_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
scale_fill_viridis(name = "Flower treatment", discrete = TRUE, begin =0.3, end = 0.8) +
theme(legend.position = "top",
legend.background = element_rect(fill=alpha('gray95', 1)),
legend.direction="horizontal")
g0IT
ggsave(g0IT, filename = file.path(figDir, "WeightedSham_Amp_IT_SUPP.pdf"), width =5, height = 3.6)
# make plot with rug
weight_rug <- g0IT + geom_rug(data = newdf3[!duplicated(newdf3$IT),], inherit.aes = FALSE, aes(x = IT))
weight_rug
ggsave(weight_rug, filename = file.path(figDir, "WeightedSham_Amp_IT_SUPP_rug.pdf"), width =5, height = 3.6)
Fig2b <- weight_rug
ITmean## [1] 3.965833g22 <- g0 +
annotate(geom="text", x=c(1,2), y=c(0, 0) + 40, label=c("a", "b"),
color="black")
ggsave(filename = file.path(figDir, "WeightedSham_Amp_pointWhiskers_annot.pdf"), width =5, height = 3.6)
## add raw data
g1 <- g0 + geom_point(data = newdf3, aes(x = treatment, y = amp_acc, color = treatment), position = position_jitter(width = 0.1, height = 6), alpha = 0.4, pch = 16, size = 0.2)
g1
ggsave(filename = file.path(figDir, "WeightedSham_amp_pointWhiskers_rawData.pdf"), width =5, height = 3.6)Put two plots into a single figure
major break – below this line is the first method I used
this is almost identical to the code above
Modeling frequency with lmer
Use BIC to select model (decide what interactions and covariates to use)
Make sure that REML = FALSE when comparing BIC values
Start with the biggest model of interest, and then see what predictors can be removed
# interaction that may be important, based on domain knowledge
m0 = lmer(freq ~ treatment*IT+ hive + (1|beeID), data = new_df, REML = FALSE)
# no interaction
m1 = lmer(freq ~ treatment+IT+ hive + (1|beeID), data = new_df, REML = FALSE)
BIC(m0, m1) # stay with m1 -- no interaction## df BIC
## m0 7 25187.77
## m1 6 25184.69anova(m0, m1) # this p-value is very borderline -- we're being ## Data: new_df
## Models:
## m1: freq ~ treatment + IT + hive + (1 | beeID)
## m0: freq ~ treatment * IT + hive + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m1 6 25150 25185 -12569 25138
## m0 7 25147 25188 -12567 25133 4.6848 1 0.03043 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# conservative to avoid overfitting by using BIC
m2 = lmer(freq ~ hive + IT+ (1|beeID), data = new_df, REML = FALSE)
BIC(m1, m2) # treatment doesn't make the model better## df BIC
## m1 6 25184.69
## m2 5 25178.53anova(m1, m2) # p-value for paper -- probably don't need to report## Data: new_df
## Models:
## m2: freq ~ hive + IT + (1 | beeID)
## m1: freq ~ treatment + IT + hive + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m2 5 25150 25178 -12570 25140
## m1 6 25150 25185 -12569 25138 1.6039 1 0.2054# p-value for hive
m3 = lmer(freq ~ treatment + (1|beeID), data = new_df, REML = FALSE)
anova(m1, m3)## Data: new_df
## Models:
## m3: freq ~ treatment + (1 | beeID)
## m1: freq ~ treatment + IT + hive + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## m3 4 25146 25169 -12569 25138
## m1 6 25150 25185 -12569 25138 0.1592 2 0.9235# diagnostics -- use REML = TRUE
m1 <- update(m1, .~., REML =TRUE)
summary(m1) # summary for paper## Linear mixed model fit by REML ['lmerMod']
## Formula: freq ~ treatment + IT + hive + (1 | beeID)
## Data: new_df
##
## REML criterion at convergence: 25115.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3676 -0.4684 0.1873 0.6825 2.3319
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 954.3 30.89
## Residual 2357.8 48.56
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 355.173 61.937 5.734
## treatmentWeighted 2.614 2.065 1.266
## IT -1.833 15.543 -0.118
## hive4 -4.129 11.398 -0.362
##
## Correlation of Fixed Effects:
## (Intr) trtmnW IT
## trtmntWghtd -0.002
## IT -0.995 -0.016
## hive4 -0.047 0.000 -0.009plot(m1)
qqnorm(ranef(m1)$beeID[[1]])
qqline(ranef(m1)$beeID[[1]])
sjp.lmer(m1, type = "re", sort = TRUE) # plot random effects to find any outliers## Plotting random effects...
sjp.lmer(m1, type = 'fe', sort = TRUE, p.kr = FALSE) # plot fixed effects## Computing p-values via Wald-statistics approximation (treating t as Wald z).
Bootstrap CI’s for figure for paper
# set number of bootstrap replicates for models
nbootSims = 1000
table(new_df$hive) # more trials from hive 3##
## 3 4
## 1644 716# using hive 3, since it's the one with the most data
# however, hive doesn't affect model anyway
# calculate an average IT for prediction
ITmean = mean(tapply(new_df$IT, INDEX = new_df$beeID, FUN = function(x) x[1] ))
pframe <- data.frame(treatment = levels(droplevels(new_df$treatment)),
IT = ITmean,
hive = factor(3, levels = levels(new_df$hive)),
beeID = 99999)
pframe$freq <- 0
pp <- predict(m1, newdata = pframe, re.form=NA, type = 'response') # re.form sets all random effects to 0
### Calculate CI's (using bootstrap, not accounting for random effects)
bb2 <- bootMer(m1, FUN=function(x) predict(x, pframe, re.form=NA, type = 'response'), nsim = nbootSims)
print(paste("Number of bootstrap samples", nrow(bb2$t)))## [1] "Number of bootstrap samples 1000"bb2_se <-apply(bb2$t,2,function(x) quantile(x, probs = c(0.025, 0.975)))
pframe$blo<-bb2_se[1,]
pframe$bhi<-bb2_se[2,]
pframe$predMean <- pp
pframe <- pframe[, c('treatment', "blo", "bhi", "predMean")]
pframe## treatment blo bhi predMean
## 1 Sham 335.3492 359.8953 347.9021
## 2 Weighted 337.7346 363.1810 350.5156Make frequency plots for paper
# "Mean and bootstrap CI based on fixed-effects uncertainty ONLY"
g0 <- ggplot(pframe, aes(x=treatment, y=predMean))+
geom_point()+
labs(y = "Sonication frequency (Hz)", x = "Flower treatment") +
geom_errorbar(aes(ymin = blo, ymax = bhi), width = 0.1)
g0
ggsave(plot = g0, filename = file.path(figDir, "HeavyLight_PredsAndCI_freq.pdf"), width =4, height = 3)Modeling amplitude with lmer
# log transform for acceleration helps model fit better
# start with large model (including interaction)
ma0 = lmer(log(amp_acc) ~ treatment * IT + hive + (1|beeID), data = new_df, REML = FALSE)
ma1 = lmer(log(amp_acc) ~ treatment + IT + hive + (1|beeID), data = new_df, REML = FALSE)
BIC(ma0, ma1) # interaction, ma0, is better## df BIC
## ma0 7 4583.334
## ma1 6 4595.150# pval for interaction (in case paper needs it)
anova(ma0, ma1)## Data: new_df
## Models:
## ma1: log(amp_acc) ~ treatment + IT + hive + (1 | beeID)
## ma0: log(amp_acc) ~ treatment * IT + hive + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma1 6 4560.6 4595.1 -2274.3 4548.6
## ma0 7 4543.0 4583.3 -2264.5 4529.0 19.582 1 9.639e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ma2 <- update(ma0, .~. - hive)
BIC(ma0, ma2) # hive not important## df BIC
## ma0 7 4583.334
## ma2 6 4576.547#pval for hive
anova(ma0, ma2)## Data: new_df
## Models:
## ma2: log(amp_acc) ~ treatment + IT + (1 | beeID) + treatment:IT
## ma0: log(amp_acc) ~ treatment * IT + hive + (1 | beeID)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ma2 6 4541.9 4576.5 -2265.0 4529.9
## ma0 7 4543.0 4583.3 -2264.5 4529.0 0.979 1 0.3224# fit with reml = TRUE for summarizing
ma3 <- update(ma2,.~., REML = TRUE)
summary(ma3) # final model to report## Linear mixed model fit by REML ['lmerMod']
## Formula: log(amp_acc) ~ treatment + IT + (1 | beeID) + treatment:IT
## Data: new_df
##
## REML criterion at convergence: 4545.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0179 -0.5395 0.1071 0.6826 2.6697
##
## Random effects:
## Groups Name Variance Std.Dev.
## beeID (Intercept) 0.07463 0.2732
## Residual 0.38434 0.6200
## Number of obs: 2360, groups: beeID, 36
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.63087 0.58488 4.498
## treatmentWeighted -1.60422 0.30031 -5.342
## IT 0.05653 0.14700 0.385
## treatmentWeighted:IT 0.33294 0.07515 4.430
##
## Correlation of Fixed Effects:
## (Intr) trtmnW IT
## trtmntWghtd -0.301
## IT -0.996 0.300
## trtmntWg:IT 0.302 -0.996 -0.303# diagnostics
plot(ma3)
qqnorm(ranef(ma3)$beeID[[1]])
qqline(ranef(ma3)$beeID[[1]])
sjp.lmer(ma3) # plot random effects to find any outliers## Plotting random effects...
sjp.lmer(ma3, type = 'fe', sort = TRUE, p.kr = FALSE) # plot fixed effects## `sjp.lmer()` will become deprecated in the future. Please use `plot_model()` instead.## Computing p-values via Wald-statistics approximation (treating t as Wald z).
Bootstrap CI’s for amplitude for figure for paper
# set number of bootstrap replicates for models
nbootSims2 = 1000
# using hive 3, since it's the one with the most data
pframe <- data.frame(treatment = levels(droplevels(new_df$treatment)), IT = ITmean, hive = factor(3, levels = levels(new_df$hive)), beeID = 99999)
pframe$amp_acc <- 0
# exponentiate to put on original scale
pp <- exp(predict(ma3, newdata = pframe, re.form=NA, type = 'response')) # re.form sets all random effects to 0
### Calculate CI's (using bootstrap, not accounting for random effects)
bb2 <- bootMer(ma3, FUN=function(x) predict(x, pframe, re.form=NA, type = 'response'), nsim = nbootSims2)
print(paste("Number of bootstrap samples", nrow(bb2$t)))## [1] "Number of bootstrap samples 1000"bb2_se <-apply(bb2$t,2,function(x) quantile(x, probs = c(0.025, 0.975)))
pframe$blo<- exp(bb2_se[1,]) # exponentiate to put on original scale
pframe$bhi<- exp(bb2_se[2,])
pframe$predMean <- pp
pframe <- pframe[, c('treatment', "blo", "bhi", "predMean")]
pframe## treatment blo bhi predMean
## 1 Sham 31.55900 37.97060 34.75029
## 2 Weighted 23.82485 28.84456 26.16290Make amplitude plots for paper
# "Mean and bootstrap CI based on fixed-effects uncertainty ONLY"
# Holding IT = meanIT
print(ITmean)## [1] 3.965833ga0 <- ggplot(pframe, aes(x=treatment, y=predMean))+
geom_point()+
labs(y = expression ("Sonication acceleration "(m~s^{-2})), x = "Flower treatment") +
geom_errorbar(aes(ymin = blo, ymax = bhi), width = 0.1) +
annotate(geom="text", x=c(1,2), y=c(0, 0) + 40, label=c("a", "b"),
color="black")
ga0
ggsave(plot = ga0, filename = file.path(figDir, "HeavyLight_PredsAndCI_amp.pdf"), width =4, height = 3)Put two plots into a single figure
# refref: note I might want to align these two figure for paper (in one plot)
# WeightedSham_Amp_pointWhiskers_BW.pdf
# WeightedSham_Freq_pointWhiskers_BW.pdf
pfreq <- Fig2a
pamp <- Fig2b + theme(legend.position = c(.5,.85)) + ylim(c(10/2,55/2))
aa <- plot_grid(pfreq, pamp, align = 'h', axis = 'l', rel_widths = c(1,2))
ggdraw(aa)
ac <- plot_grid(pfreq, pamp, align = 'h', axis = 'l', rel_widths = c(1,2), labels = "AUTO")
ggdraw(ac)
save_plot(file.path(figDir, "CombinedFreqAmp_weightedSham4_noxlab_IT.pdf"), plot = aa, base_width = 7, base_height = 3)
save_plot(file.path(figDir, "CombinedFreqAmp_weightedSham4_annot_IT.pdf"), plot = ac, base_width = 7, base_height = 3)sessionInfo()## R version 3.4.2 (2017-09-28)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS High Sierra 10.13.3
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] cowplot_0.9.1 viridis_0.4.0 viridisLite_0.2.0
## [4] gamm4_0.2-5 mgcv_1.8-20 nlme_3.1-131
## [7] effects_4.0-0 carData_3.0-0 plyr_1.8.4
## [10] multcomp_1.4-8 TH.data_1.0-8 MASS_7.3-47
## [13] survival_2.41-3 mvtnorm_1.0-6 sjPlot_2.4.0
## [16] lme4_1.1-14 Matrix_1.2-11 reshape2_1.4.2
## [19] ggplot2_2.2.1
##
## loaded via a namespace (and not attached):
## [1] pbkrtest_0.4-7 RColorBrewer_1.1-2 rprojroot_1.2
## [4] tools_3.4.2 TMB_1.7.11 backports_1.1.1
## [7] R6_2.2.2 sjlabelled_1.0.5 DT_0.2
## [10] lazyeval_0.2.1 colorspace_1.3-2 nnet_7.3-12
## [13] gridExtra_2.3 tidyselect_0.2.3 mnormt_1.5-5
## [16] compiler_3.4.2 sandwich_2.4-0 labeling_0.3
## [19] scales_0.5.0 lmtest_0.9-35 psych_1.7.8
## [22] blme_1.0-4 stringr_1.2.0 digest_0.6.12
## [25] foreign_0.8-69 minqa_1.2.4 rmarkdown_1.8
## [28] stringdist_0.9.4.6 pkgconfig_2.0.1 htmltools_0.3.6
## [31] pwr_1.2-1 htmlwidgets_0.9 rlang_0.1.4
## [34] shiny_1.0.5 bindr_0.1 zoo_1.8-0
## [37] dplyr_0.7.4 magrittr_1.5 modeltools_0.2-21
## [40] bayesplot_1.4.0 Rcpp_0.12.13 munsell_0.4.3
## [43] abind_1.4-5 prediction_0.2.0 stringi_1.1.6
## [46] yaml_2.1.14 merTools_0.3.0 snakecase_0.5.1
## [49] grid_3.4.2 parallel_3.4.2 sjmisc_2.6.2
## [52] forcats_0.2.0 lattice_0.20-35 ggeffects_0.2.2
## [55] haven_1.1.0 splines_3.4.2 sjstats_0.12.0
## [58] knitr_1.17 codetools_0.2-15 stats4_3.4.2
## [61] glue_1.2.0 evaluate_0.10.1 modelr_0.1.1
## [64] nloptr_1.0.4 httpuv_1.3.5 gtable_0.2.0
## [67] purrr_0.2.4 tidyr_0.7.2 assertthat_0.2.0
## [70] mime_0.5 coin_1.2-1 xtable_1.8-2
## [73] broom_0.4.2 survey_3.32-1 coda_0.19-1
## [76] tibble_1.3.4 arm_1.9-3 glmmTMB_0.1.4
## [79] bindrcpp_0.2